example of problem solving in multiplication of decimals

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Algebra basics

Course: algebra basics   >   unit 1.

• Adding decimals: 9.087+15.31
• Adding decimals: 0.822+5.65
• Adding decimals: thousandths
• Subtracting decimals: 9.57-8.09
• Subtracting decimals: 39.1 - 0.794
• Subtracting decimals: thousandths

Multiplying decimals example

• Multiplying challenging decimals
• Decimal multiplication place value
• Dividing decimals with hundredths
• Dividing by a multi-digit decimal
• Dividing decimals: hundredths

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Video transcript

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Multiplying decimals

Here you will learn about multiplying decimals, including how to multiply decimals by a whole number and multiply decimals by decimals.

Students will first learn about multiplying decimals in 5th grade math as part of their work in number and operations.

What is multiplying decimals?

Multiplying decimals is when you multiply numbers involving decimals.

Let’s look at strategies for multiplying decimal numbers.

Common Core State Standards

How does this relate to 5th and 6th grade math?

• Grade 5: Number & Operations Base Ten (5.NBT.B.7) Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
• Grade 6: The Number System (6.NS.B.3) Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

[FREE] Multiplying Decimals Worksheet (Grade 5 to 6)

Use this worksheet to check your grade 5 to 6 students’ understanding of multiplying decimals. 15 questions with answers to identify areas of strength and support!

How to multiply decimals

In order to multiply decimals using the standard algorithm.

Stack the number with the most digits on top.

• Multiply as if the numbers were multi-digit whole numbers, regrouping when necessary.

Count the number of digits after the decimal point for each factor.

• Put the same number of digits after the decimal point for the product.

In order to solve decimal multiplication word problems.

• Create an equation to model the problem.

Multiply as if the numbers were multi-digit whole numbers, regrouping when necessary.

• Put the same number of digits behind the decimal as the product.

Label the product.

Multiplying decimal examples

Example 1: multiplying a decimal number by a decimal number.

Find the product of 0.8 \times 0.4 .

Both factors have the same number of digits, so it does not matter which one is on top.

2 Multiply as if the numbers were multi-digit whole numbers, regrouping when necessary.

3 Count the number of digits after the decimal point for each factor.

Together, there are two numbers after the decimal point.

4 Put the same number of digits after the decimal point for the product.

Move the decimal point two decimal places. The product will have two digits after the decimal point.

The product is 0.32.

On the hundredths grid, look at the overlapped shaded region. There are 32 squares in that area which is 32 hundredths or 0.32

Example 2: multiplying a decimal number by a whole number

Find the product of 1.21 \times 3 .

1.21 has more digits than 3, so 1.21 will be on top.

In total, there are two decimal places after the decimal point.

Put the same number of digits behind the decimal for the product.

The product is 3.63

Looking at the hundredths grids, you can see there are 3 groups of 1.21 that represent 363 shade squares, 363 squares = \; 3.63

Example 3: multiplying a decimal number by a decimal number

Find the product of 3.4 \times 43.2 .

43.2 has more digits than 3.4, so it will go on top.

The product is 146.88

Example 4: multiplying a decimal by a decimal

Solve the multiplication problem, 1.642 \times 32.7 .

1.642 has more digits than 32.7, so it will go on top.

In total, there are four decimal places after the decimal point.

Move the decimal point four decimal places. The answer has four digits after the decimal point.

The product is 53.6934

Example 5: word problem multiplying a whole number by a decimal number

Kit claims she has 4.5 times as many songs on her playlist as Kai. If Kai has 48 songs on his playlist, how many does Kit have on hers?

Create an equation to model the problem

4.5 \times 48 = \; ?

48 and 4.5 have the same number of digits. It does not matter which one goes on top.

In total, there is one decimal place after the decimal point.

Move the decimal point one decimal place. The product will have one digit after the decimal point.

The product is 216.0 or 216

Kit has 216 songs on her playlist.

Example 6: word problem multiplying decimal number by a decimal number

On Jupiter, objects weigh about 2.4 times as much as they do on Earth. How much would a 9.45 -pound puppy weigh on Jupiter?

9.45 \times 2.4 = \; ?

9.45 has more digits, so it will go on top.

In total, there are three decimal places after the decimal point.

Move the decimal point three decimal places. The product will have three digits after the decimal point.

The product is 22.680 or 22.68

The puppy will weigh 22.68 pounds on Jupiter.

Teaching tips for multiplying decimals

• In 5th grade math, students are first taught about decimal multiplication using visual models such as hundredths grids. As they develop understanding they are able to connect the algorithm of multi-digit multiplication to the multiplication of decimals.
• Explore other strategies for decimal multiplication such as partial products, which emphasize the distributive property and may be easier for students to understand.
• Although practicing the skill of decimal multiplication is important, do not rely on practice worksheets to develop deep understanding. Using visual models, hands-on activities, and digital games are very effective alternatives to multiplication problem worksheets.

Our favorite mistakes

• Placing the decimal point in the wrong position in the answer (product) It is important to remember to count the number of places that are in both factors. The total number of digits to the right of the decimal point is how many the answer should have to the right of the decimal point.
• Leaving the decimal point out completely
• Thinking that the decimal points of the products need to line up before multiplying like they do in addition of decimals

Related lessons on decimals

• Multiplying and dividing decimals
• Adding decimals
• Decimal places
• Decimal number line
• Decimal place value
• Dividing decimals
• Adding and subtracting decimals
• Subtracting decimals
• Comparing decimals

Practice multiplying decimals questions

1. Find the product of the numbers.

4.37 has more digits than 14, so it will go on top.

  In total, there are two decimal places after the decimal point. Move the decimal point two decimal places. The answer will have two digits after the decimal point.   Product = \; 61.18

2. Find the product of the two numbers.

5.21 has more digits than 1.6, so it will go on top.

There are a total of three digits after the decimal point. Move the decimal point three decimal places  

Product = \; 8.336

3. Find the product of the numbers.

0.264 has more digits than 1.1, so it will go on top.

There are a total of four digits after the decimal point. Move the decimal point four decimal places.

Product = \; 0.2904

4. Kaylee went to the bookstore to buy 6 books she needed for her class. If the books cost \$17.25 each, how much did she spend on her books?

There are a total of two digits after the decimal point. Move the decimal point two decimal places.

Kaylee will spend \$103.25 on the 6 books.

5. The local farmer sold 13.2 pounds of tomatoes. She sold 2.5 times more apples than tomatoes. How many pounds of apples did she sell?

33.3 pounds

33.33 pounds

2.5 times more pounds of apples were sold than tomatoes. Multiply 2.5 times 13.2.  

33.00 = 33 pounds of apples were sold.

Multiplying decimals FAQs:

Yes, in 6th grade, you will become very familiar with changing decimals to fractions and fractions to decimals. However, there are certain situations where keeping the number as a decimal might be easier.

Work typically involves multiplying numbers that have values in either the tenths place, hundredths place and/or the thousandths place.

\begin{aligned} & \quad \quad \bf{1.3} \quad \quad \textbf{×} \quad \quad \bf{3.4} \quad \quad \textbf{=} \quad \quad \bf{4.08} \\ & \quad \quad \;\; \text{⇧} \quad \quad \quad \quad \quad \; \text{⇧} \quad \quad \quad \quad \quad \;\; \text{⇧}\\ & \text{multiplicand} \quad \; \text{multiplier} \quad \quad \text{product} \end{aligned}

The next lessons are

• Converting fractions, decimals, and percentages
• Algebraic expression
• Math equations
• Rounding decimals

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Multiplying Decimals

Multiply without the decimal point, then re-insert it in the correct spot!

How to Multiply Decimals

Just follow these steps:

• Multiply normally, ignoring the decimal points.
• Then put the decimal point in the answer - it will have as many decimal places as the two original numbers combined.

In other words, just count up how many numbers are after the decimal point in both numbers you are multiplying, then the answer should have that many numbers after its decimal point.

Example: Multiply 0.03 by 1.1

How does it work.

Because when you multiply without the decimal point, you are really shifting the decimal point to the right to get it out of the way :

Then we do the (now easy) multiplication:

3. × 11. = 33.

But remember, we did 3 Moves of the decimal point, so we need to undo that:

Here are some more examples:

Example: Multiply 0.25 by 0.2

Example: multiply 102 by 0.22, common sense.

As a final check you can put your "common sense" hat on and think "is that the right size?" , because you don't want to pay ten times too much for anything, nor get only one-tenth of what you need!

And that's all.

Just remember: the answer should have the same number of decimal places as are in both the numbers you are multiplying.

Fun teaching resources & tips to help you teach math with confidence

{FREE} Multiplying Decimals Word Problems Set

Whether our kids want to admit it or not, decimals are a part of our everyday life. And it’s important that they feel confident doing basic computations with decimals. Even if they start to use a calculator, they still need to understand how to rightly apply operations with decimals to solve real world problems. If they don’t know whether to multiply or add, using a calculator isn’t going to help. So I hope this free set of multiplying decimals word problems provides a chance for some quick, low-prep practice.

* Please Note : This post contains affiliate links which support the work of this site. Read our full disclosure here .*

Multiplying Decimals Word Problems:

This set of word problems is actually a sample from my ‘Making Sense of Word Problems’ course . In that course, I explain the different types and structures for word problems .

When you consider multiplication and division problems, there are actually 9 different types or problem structures for a multiplication/division problem.

This set of 27 decimal word problems covers all the different structures, which kids can solve using multiplication and division.

Each page includes 3 problems , with space for kids to write out their thinking and solution. However, you could also cut the pages into strips to assign one problem at a time.

The download also includes an answer key , making it easy for you to print and use with your students.

Ways to Incorporate More Word Problem Practice:

There are a lot of different ways you can include word problem practice into your math routine, but here are some ideas to get you started. Or just provide some ideas you may not have thought of.

• At the start of a new unit: Although most curricula or textbooks will save word problems for last, I actually think you should begin a unit by presenting a problem for kids to solve. This does not necessarily have to be a word problem, but with multiplication and division involving fractions and decimals, I think these skills are best learned in context . So even if you have not given students an example or method for solving, this will encourage them to think and apply what they know to come up with their own ideas and strategies.
• As a daily challenge problem: Another idea is to have a ‘problem of the day’ word problem for kids, perhaps when they come into class. This is a great way to not only work on word problems, but also review skills, because this doesn’t necessarily need to be related to your lesson that day. This set of word problems can easily be cut into strips so kids can glue the problem into their notebook or math journal each day.
• Math practice for a sub day: Not sure what to plan for your substitute while you’re out? Why not give kids a set of related word problems? Let them work independently or in small groups . Then when you return you can discuss the different problems, how to multiply and divide decimals or different strategies kids used.
•  As homework: Lastly, assigning a small set of related word problems as homework provides practice for kids independently, but not an overwhelming amount.

But however you include word problems as you explore multiplying decimals or dividing decimals , I hope this set of 27 problems provides a quick and easy resource for you.

{Click HERE to go to my shop and grab the FREE set of Multiplying Decimals Word Problems}

*pssst: looking for even more word problem resources check out the complete course to help you and your students make sense of word problems., find more free word problem resources below:.

• Word problem solving templates
• I Notice…I Wonder Routine for solving problems | Journal for kids
• Pythagorean Theorem word problems
• Lemonade stand word problems | time & money
• Two step problems set | multiplication & subtraction of whole numbers

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Multiplying Decimals

Multiplying decimals is very important when we talk about the grouping of items. Suppose you have to distribute 0.25 part of a chocolate bar to each child and there is a total of 12 children. How many chocolate bars would you need? To find the number of chocolate bars required, we have to multiply 12 by 0.25. Multiplication of decimals is done by ignoring the decimal point and multiply the numbers, and then the number of decimal places in the product is equal to the total number of decimal places in both the given numbers.

How to Multiply Decimals?

Multiplying Decimals has the same procedure as that of multiplication of the whole numbers, except the placement of the decimal point in the product. In our everyday life, we have come across various instances where we have to use the multiplication operation on two numbers out of which at least one or both are decimal numbers. Imagine going out with your friend for lunch. You both order a platter costing $6.75 each. The total bill amounts to $15.75, including the taxes. To calculate the total cost of the platter in the bill, you need to multiply $6.75 × 2. Similarly, suppose you plan to gift your mother a flower bouquet on her birthday. Each flower costs $0.75 and you buy a total of 6 flowers. To find the total cost of the bouquet, you need to multiply $0.75 × 6. The above examples follow the application of multiplying decimals.

Multiplying Decimals with Whole Numbers

Multiplying decimals with whole numbers is similar to the multiplication of whole numbers , the only difference being in the placement of the decimal point. The following steps can be followed to multiply decimals with whole numbers:

• Step 1: Initially, ignore the decimal point and multiply the two numbers normally.
• Step 2: After multiplication, count the number of decimal places in the decimal number. The product obtained after multiplication will have the same number of decimal places.
• Step 3: Place the decimal point in the obtained product following Step 2 .

Let us understand a real-life situation of multiplying decimal numbers with whole numbers. A class of 15 students decided to contribute to a relief fund. Each student made a contribution of $6.5. What was the total amount collected from the whole class? Here, the contribution made by one student = $6.5. Total contribution made by 15 students = 6.5 × 15= $97.5.

Multiplying Decimals by 10 100 and 1000

While multiplying any decimal by 10, 100, 1000, or any other power of 10, we just simply shift the decimal point towards the right as many places as the number of zeros in the power of 10.

• If we multiply a decimal by 10, we shift the decimal point one place towards the right, as there is 1 zero in the number 10.
• If we multiply any decimal by 100, we shift the decimal point two places towards the right.
• Similarly, if we multiply a decimal by 1000, we shift the decimal point by three places towards the right, and so on.

For example, 2.32 × 10 = 23.2, 2.32 ×100 = 232, 2.32 × 1000= 2320.

Multiplying Two Decimals Numbers

This section will help you to learn about the multiplication of two decimal numbers. It is the same as that of the whole number, but the only difference is that in this we have to take the sum of the total number of decimal places in both the given numbers and that needs to be equal to the number of decimal places in the product . To multiply two decimals, follow the steps listed below:

• Step 2: After multiplication, count the total number of decimal places in both the numbers. The product obtained after multiplication will have this total number of decimal places.

Let us see the multiplication of two decimal numbers in the image given below:

Examples of Multiplying Decimals:

1. Multiply 0.567 and 13.065

Therefore, 0.567 × 13.065 = 7.407855. There are 6 digits after the decimal point.

2. Find the product of 16.45 and 8.5

Therefore, 16.45 × 8.5 = 139.825. The product has 3 digits after the decimal point.

Important Notes:

These are few important notes related to the concept of multiplying decimals. Have a look!

• The decimal multiplication follows the same procedure as the multiplication of whole numbers.
• The decimal point should be placed in the product in such a way that, the product has a number of decimal places equal to the sum of decimal places of all the multiplicands and the multipliers.
• Make sure you keep all the zeros in the product while placing the decimal point.
• If the product has more decimal places than the number of digits, zeros can be inserted on the left before placing the decimal point in the product.
• The trailing zeros in the resultant product can be dropped.

Try and Solve these Challenging Questions:

• Charlie is paid $17.45 per hour and worked 42.5 hours last week. How much money did he earn last week (rounded to the nearest cent)?
• What is the total distance covered by a car if it traveled with a speed of 31.5 miles/hour for 7 hours and 15 minutes?

Multiplying Decimals Related Topics

Check these articles related to multiplying decimals.

• Dividing Decimals Calculator
• Adding Decimals Calculator
• Decimals and Fractions
• How to Add Decimals?
• Dividing Decimals
• Addition and Subtraction of Decimals

Multiplying Decimals Examples

Example 1: Rose is learning decimal multiplication. Can you help her multiply 0.6748 with 14.945?

Let's see how to multiply 0.6748 and 14.945.

Note: The trailing zeros can be dropped. Therefore, 0.6748 × 14.945 = 10.084886.

Example 2: Gracy went to the grocery store with her mother. Her mother bought 15 apples costing $1.25 each. Help Gracy to calculate the amount her mother needs to pay by using the concept of multiplying decimals.

We have, cost of one apple = $1.25. Thus, cost of 15 apples = $1.25 × 15. Therefore, the cost of 15 apples is $18.75.

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Practice Questions on Multiplying Decimals

Faqs on multiplying decimals, how do you multiply a decimal number by a whole number.

To multiply a decimal number by a whole number, follow the steps given below:

• Step-1: Ignore the decimal point and multiply both the numbers.
• Step-2: Count the number of decimal places in the decimal number.
• Step-3: Then, place the decimal point in the product such that the number of decimal places in the product and the original decimal number should be the same.

How do you Multiply Decimals by 1000?

To multiply decimals with 1000, shift the decimal point three places towards the right, as there are three zeroes in 1000.

How to Teach Multiplying Decimals?

Let us see how to teach decimal multiplication to learners through the following ways:

• First, make students understand the meaning of decimal multiplication with the help of demonstration and visualization.
• Second, introduce the steps to multiply two decimal numbers to the students.
• Give practice questions.

What is the Rule of Multiplying Decimals?

The multiplying decimals rules are given below:

Rules for Multiplication of Decimals:

• Perform multiplication in a similar way as with whole numbers.
• If the product has more decimal places than the number of digits, zeros can be inserted before placing the decimal point in the product such that only one zero will be there at the left of the decimal point and the decimal places in the product will be equal to the total number of decimal places in both the numbers.
• The trailing zeros in the fractional part of the resultant product can be dropped.

How do you Multiply Decimals Less Than 1?

To multiply two decimals less than 1, follow the steps given below:

• Step 1: Initially, Ignore the decimal point and multiply the two numbers normally.
• Step 2: After multiplication, count the total number of decimal places in multiplicand and the multiplier. The product obtained after multiplication will have this total number of decimal places.
• Step 3: Place the decimal point in the obtained product following Step2 .

For example: 0.2 × 0.4 = 0.08.

How do you Multiply Positive and Negative Decimals?

Positive and negative decimals are multiplied in a similar way as two decimals.

• Multiply both the numerical parts as we do in normal decimal multiplication.
• Since the product of one negative number and one positive number is negative, thus retain the negative sign before the numerical part of the product hence obtained.

For example, -0.5 × 0.3 = -0.15.

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How to Perform Operations of Decimals: Word Problems

Greetings, budding mathematicians! Today, we're going to jump into an adventure with decimals. Working with decimals is a fundamental math skill that you'll use in many aspects of life, from managing money to measuring distances.

Introduction to Decimal Operations

First things first, let’s talk about decimals. A decimal is a way of representing a number that’s less than one, or a number that’s a whole and a fraction together. When you work with decimals, the same rules apply as when you’re working with whole numbers, but the decimal point plays a crucial role.

There are four major operations that you can perform on decimals:

• Subtraction
• Multiplication

Now, let’s tackle some word problems involving decimal operations.

Step-By-Step Guide to Solving Word Problems with Decimal Operations

Step 1: understand the problem.

First and foremost, carefully read through the problem. Identify what you know and what you need to find out.

Step 2: Plan the Solution

Next, decide which operation (addition, subtraction, multiplication, or division) will help you solve the problem. This will depend on what the problem is asking.

Step 3: Carry Out the Operation

Perform the operation on the decimals. Remember to align the decimal points when you’re adding or subtracting, and apply the rules for multiplication and division of decimals correctly.

Step 4: Check the Answer

Finally, check if your answer makes sense in the context of the problem.

Consider this problem: Laura bought \(2.3\) kilograms of apples and \(1.5\) kilograms of grapes. How many kilograms of fruit did she buy in total?

Step 1: Understand that you know the weight of apples and grapes separately, and you need to find the total weight.

Step 2: Realize that to find the total, you need to add the weights together.

Step 3: Add the weights: \(2.3\ kg + 1.5\ kg = 3.8\ kg\).

Step 4: Check that the answer makes sense. Laura bought \(2.3\ kg\) of apples and \(1.5\ kg\) of grapes, so it makes sense that she bought \(3.8\ kg\) in total.

Keep practicing with different word problems, and you’ll get the hang of decimal operations in no time. Remember, the more you practice, the better you’ll get. Happy calculating!

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6.5: Multiplication of Decimals

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• Save as PDF
• Page ID 48868

• Denny Burzynski & Wade Ellis, Jr.
• College of Southern Nevada via OpenStax CNX

Learning Objectives

• understand the method used for multiplying decimals
• be able to multiply decimals
• be able to simplify a multiplication of a decimal by a power of 10
• understand how to use the word "of" in multiplication

The Logic Behind the Method

Consider the product of 3.2 and 1.46. Changing each decimal to a fraction, we have

\(\begin{array} {rcl} {(3.2)(1.46)} & = & {3 \dfrac{2}{10} \cdot 1 \dfrac{46}{100}} \\ {} & = & {\dfrac{32}{10} \cdot \dfrac{146}{100}} \\ {} & = & {\dfrac{32 \cdot 146}{10 \cdot 100}} \\ {} & = & {\dfrac{4672}{1000}} \\ {} & = & {4 \dfrac{672}{1000}} \\ {} & = & {\text{four and six hundred seventy-two thousandths}} \\ {} & = & {4.672} \end{array}\)

Thus, \((3.2)(1.46) = 4.672\)

Notice that the factor

\(\left \{ \begin{array} {c} {\text{3.2 has 1 decimal place,}} \\ {\text{1.46 has 2 decimal places,}} \\ {\text{and the product}} \\ {\text{4.672 has 3 decimal places.}} \end{array} \right \} 1 + 2 = 3\)

Using this observation, we can suggest that the sum of the number of decimal places in the factors equals the number of decimal places in the product.

The Method of Multiplying Decimals

Method of Multiplying Decimals

To multiply decimals:

• Multiply the numbers as if they were whole numbers.
• Find the sum of the number of decimal places in the factors.
• The number of decimal places in the product is the sum found in step 2.

Sample Set A

Find the following products.

\(6.5 \cdot 4.3\)

Thus, \(6.5 \cdot 4.3 = 27.95.\)

\(23.4 \cdot 1.96\)

Thus, \(23.4 \cdot 1.96 = 45.864.\)

Find the product of 0.251 and 0.00113 and round to three decimal places.

Now, rounding to three decimal places, we get

Practice Set A

\(5.3 \cdot 8.6\)

\(2.12 \cdot 4.9\)

\(1.054 \cdot 0.16\)

\(0.00031 \cdot 0.002\)

Find the product of 2.33 and 4.01 and round to one decimal place.

\(10 \cdot 5.394\)

\(100 \cdot 5.394\)

\(1000 \cdot 5.394\)

\(10,000 \cdot 5.394\)

Calculators

Calculators can be used to find products of decimal numbers. However, a calculator that has only an eight-digit display may not be able to handle numbers or products that result in more than eight digits. But there are plenty of inexpensive ($50 - $75) calculators with more than eight-digit displays.

Sample Set B

Find the following products, if possible, using a calculator.

\(2.58 \cdot 8.61\)

The product is 22.2138.

\(0.006 \cdot 0.0042\)

We know that there will be seven decimal places in the product (since \(3 + 4 = 7\)). Since the display shows 7 decimal places, we can assume the product is correct. Thus, the product is 0.0000252.

\(0.0026 \cdot 0.11976\)

Since we expect \(4 + 5 = 9\) decimal places in the product, we know that an eight-digit display calculator will not be able to provide us with the exact value. To obtain the exact value, we must use "hand technology." Suppose, however, that we agree to round off this product to three decimal places. We then need only four decimal places on the display.

Rounding 0.0003114 to three decimal places we get 0.000. Thus, \(0.0026 \cdot 0.11976 = 0.000\) to three decimal places.

Practice Set B

Use a calculator to find each product. If the calculator will not provide the exact product, round the result to four decimal places.

\(5.126 \cdot 4.08\)

\(0.00165 \cdot 0.04\)

\(0.5598 \cdot 0.4281\)

\(0.000002 \cdot 0.06\)

Multiplying Decimals by Powers of 10

There is an interesting feature of multiplying decimals by powers of 10. Consider the following multiplications.

Multiplying a Decimal by a Power of 10 To multiply a decimal by a power of 10, move the decimal place to the right of its current position as many places as there are zeros in the power of 10. Add zeros if necessary.

Sample Set C

\(100 \cdot 34.876\). Since there are 2 zeros in 100, Move the decimal point in 34.876 two places to the right.

\(1,000 \cdot 4.8058\). Since there are 3 zeros in 1,000, move the decimal point in 4.8058 three places to the right.

\(10,000 \cdot 56.82\). Since there are 4 zeros in 10,000, move the decimal point in 56.82 four places to the right. We will have to add two zeros in order to obtain the four places.

Since there is no fractional part, we can drop the decimal point.

Practice Set C

\(100 \cdot 4.27\).

\(10,000 \cdot 16.52187\).

\((10)(0.0188)\).

\((10,000,000,000)(52.7)\).

527,000,000,000

Multiplication in Terms of “Of”

Recalling that the word "of" translates to the arithmetic operation of multiplica­tion, let's observe the following multiplications.

Sample Set D

Find 4.1 of 3.8.

Translating "of" to "\(\times\)", we get

\(\begin{array} {r} {4.1} \\ {\underline{\times 3.8}} \\ {328} \\ {\underline{123\ \ }} \\ {15.58} \end{array}\)

Find 0.95 of the sum of 2.6 and 0.8.

We first find the sum of 2.6 and 0.8.

\(\begin{array} {r} {2.6} \\ {\underline{+0.8}} \\ {3.4} \end{array}\)

Now find 0.95 of 3.4

\(\begin{array} {r} {3.4} \\ {\underline{\times 0.95}} \\ {170} \\ {\underline{306\ \ }} \\ {3.230} \end{array}\)

Thus, 0.95 of \((2.6 + 0.8)\) is 3.230.

Practice Set D

Find 2.8 of 6.4.

Find 0.1 of 1.3.

Find 1.01 of 3.6.

Find 0.004 of 0.0009.

Find 0.83 of 12.

Find 1.1 of the sum of 8.6 and 4.2.

For the following 30 problems, find each product and check each result with a calculator.

Exercise \(\PageIndex{1}\)

\(3.4 \cdot 9.2\)

Exercise \(\PageIndex{2}\)

\(4.5 \cdot 6.1\)

Exercise \(\PageIndex{3}\)

\(8.0 \cdot 5.9\)

Exercise \(\PageIndex{4}\)

\(6.1 \cdot 7\)

Exercise \(\PageIndex{5}\)

\((0.1)(1.52)\)

Exercise \(\PageIndex{6}\)

\((1.99)(0.05)\)

Exercise \(\PageIndex{7}\)

\((12.52)(0.37)\)

Exercise \(\PageIndex{8}\)

\((5.116)(1.21)\)

Exercise \(\PageIndex{9}\)

\((31.82)(0.1)\)

Exercise \(\PageIndex{10}\)

\((16.527)(9.16)\)

Exercise \(\PageIndex{11}\)

\(0.0021 \cdot 0.013\)

Exercise \(\PageIndex{12}\)

\(1.0037 \cdot 1.00037\)

Exercise \(\PageIndex{13}\)

\((1.6)(1.6)\)

Exercise \(\PageIndex{14}\)

\((4.2)(4.2)\)

Exercise \(\PageIndex{15}\)

\(0.9 \cdot 0.9\)

Exercise \(\PageIndex{16}\)

\(1.11 \cdot 1.11\)

Exercise \(\PageIndex{17}\)

\(6.815 \cdot 4.3\)

Exercise \(\PageIndex{18}\)

\(9.0168 \cdot 1.2\)

Exercise \(\PageIndex{19}\)

\((3.5162)(0.0000003)\)

0.00000105486

Exercise \(\PageIndex{20}\)

\((0.000001)(0.01)\)

Exercise \(\PageIndex{21}\)

\((10)(4.96)\)

Exercise \(\PageIndex{22}\)

\((10)(36.17)\)

Exercise \(\PageIndex{23}\)

\(10 \cdot 421.8842\)

Exercise \(\PageIndex{24}\)

\(10 \cdot 8.0107\)

Exercise \(\PageIndex{25}\)

\(100 \cdot 0.19621\)

Exercise \(\PageIndex{26}\)

\(100 \cdot 0.779\)

Exercise \(\PageIndex{27}\)

\(1000 \cdot 3.596168\)

Exercise \(\PageIndex{28}\)

\(1000 \cdot 42.7125571\)

Exercise \(\PageIndex{29}\)

\(1000 \cdot 25.01\)

Exercise \(\PageIndex{30}\)

\(100,000 \cdot 9.923\)

Exercise \(\PageIndex{31}\)

\((4.6)(6.17)\)

Exercise \(\PageIndex{32}\)

\((8.09)(7.1)\)

Exercise \(\PageIndex{33}\)

\((11.1106)(12.08)\)

Exercise \(\PageIndex{34}\)

\(0.0083 \cdot 1.090901\)

Exercise \(\PageIndex{35}\)

\(7 \cdot 26.518\)

For the following 15 problems, perform the indicated operations

Exercise \(\PageIndex{36}\)

Find 5.2 of 3.7.

Exercise \(\PageIndex{37}\)

Find 12.03 of 10.1

Exercise \(\PageIndex{38}\)

Find 16 of 1.04

Exercise \(\PageIndex{39}\)

Find 12 of 0.1

Exercise \(\PageIndex{40}\)

Find 0.09 of 0.003

Exercise \(\PageIndex{41}\)

Find 1.02 of 0.9801

Exercise \(\PageIndex{42}\)

Find 0.01 of the sum of 3.6 and 12.18

Exercise \(\PageIndex{43}\)

Find 0.2 of the sum of 0.194 and 1.07

Exercise \(\PageIndex{44}\)

Find the difference of 6.1 of 2.7 and 2.7 of 4.03

Exercise \(\PageIndex{45}\)

Find the difference of 0.071 of 42 and 0.003 of 9.2

Exercise \(\PageIndex{46}\)

If a person earns $8.55 an hour, how much does he earn in twenty-five hundredths of an hour?

Exercise \(\PageIndex{47}\)

A man buys 14 items at $1.16 each. What is the total cost?

Exercise \(\PageIndex{48}\)

In the problem above, how much is the total cost if 0.065 sales tax is added?

Exercise \(\PageIndex{49}\)

A river rafting trip is supposed to last for 10 days and each day 6 miles is to be rafted. On the third day a person falls out of the raft after only \(\dfrac{2}{5}\) of that day’s mileage. If this person gets discouraged and quits, what fraction of the entire trip did he complete?

Exercise \(\PageIndex{50}\)

A woman starts the day with $42.28. She buys one item for $8.95 and another for $6.68. She then buys another item for sixty two-hundredths of the remaining amount. How much money does she have left?

Calculator Problems For the following 10 problems, use a calculator to determine each product. If the calculator will not provide the exact product, round the results to five decimal places.

Exercise \(\PageIndex{51}\)

\(0.019 \cdot 0.321\)

Exercise \(\PageIndex{52}\)

\(0.261 \cdot 1.96\)

Exercise \(\PageIndex{53}\)

\(4.826 \cdot 4.827\)

Exercise \(\PageIndex{54}\)

\((9.46)^2\)

Exercise \(\PageIndex{55}\)

\((0.012)^2\)

Exercise \(\PageIndex{56}\)

\(0.00037 \cdot 0.0065\)

Exercise \(\PageIndex{57}\)

\(0.002 \cdot 0.0009\)

Exercise \(\PageIndex{58}\)

\(0.1286 \cdot 0.7699\)

Exercise \(\PageIndex{59}\)

\(0.01 \cdot 0.00000471\)

0.0000000471

Exercise \(\PageIndex{60}\)

\(0.00198709 \cdot 0.03\)

Exercises for Review

Exercise \(\PageIndex{61}\)

Find the value, if it exists, of \(0 \div 15\).

Exercise \(\PageIndex{62}\)

Find the greatest common factor of 210, 231, and 357.

Exercise \(\PageIndex{63}\)

Reduce \(\dfrac{280}{2,156}\) to lowest terms.

\(\dfrac{10}{77}\)

Exercise \(\PageIndex{64}\)

Write "fourteen and one hundred twenty-one ten-thousandths, using digits."

Exercise \(\PageIndex{65}\)

Subtract 6.882 from 8.661 and round the result to two decimal places.

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Multiplying Decimals Word Problems Worksheets

• Pre-Algebra >
• Decimals >
• Multiplication >

If children and our free, printable multiplying decimals word problems worksheets have found harmony with each other, children and a desire to excel have found harmony with each other. The promise is an inexhaustible supply of real-world problems on decimal multiplication! Make the most of the resources presenting you with umpteen real-life scenarios on multiplying decimals by whole numbers and multiplying two decimals. Read the scenarios, boil them down to the multiplicand and multiplier, and determine the product. Get ready to tackle this pdf collection!

We recommend our decimal multiplication word problems worksheets pdf for 5th grade, 6th grade, and 7th grade kids.

Multiplying Decimals by Whole Numbers Word Problems | Customary

Lucy dropped $0.67 into a charity box. If James dropped six times the money, how much did he donate? It's $4.02. These exercises, featuring decimals and whole numbers with customary units, have more such questions.

Multiplying Decimals by Whole Numbers Word Problems | Metric

Can you imagine money, measurement, and more without decimals? The answer is a resounding "No". Let grade 5 and grade 6 kids tackle word problems involving decimals, whole numbers, and metric units.

Multiplying Decimals Word Problems | Customary

Watch grade 7 learners tackle multiplying decimals with different decimal places. Show off your skills by solving these printable multiplying decimals word problems worksheets featuring customary units.

Multiplying Decimals Word Problems | Metric

The more you practice these printable worksheets, the smarter you become at figuring out problems on multiplying two decimals. Be mindful of placing the decimal point in the product. These exercises feature metric units.

Related Printable Worksheets

▶ Multiplying Decimals Using Number Lines

▶ Multiplying Decimals by Powers of Ten

▶ Multiplying Decimals by Whole Numbers

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Decimals  - Multiplying and Dividing Decimals

Decimals  -, multiplying and dividing decimals, decimals multiplying and dividing decimals.

Decimals: Multiplying and Dividing Decimals

Lesson 3: multiplying and dividing decimals.

/en/decimals/adding-and-subtracting-decimals/content/

Multiplying with decimals

In Adding and Subtracting Decimals , you learned how to add decimal numbers. You may be able to think of times when you'd add decimals in real life. For example, let's say you go to the store and find a shirt you really like. The price tag says it costs $15.60 . You like the shirt so much that you decide to buy five of them.

To figure out the total cost, you could add the prices.

Adding this many numbers could take a long time. In the lesson on multiplication , we learned that when you multiply, you are increasing a number many times. Because all of the shirt prices are the same , multiplication could help you solve this problem a little faster.

When you multiply decimal numbers, it's helpful to set up the problem in a way that makes it easier for you to solve it one step at a time .

Click through the slideshow below to learn how to set up a multiplication problem with decimals.

Instead of adding $15.60 + $15.60 + $15.60 + $15.60 + $15.60 ...

Instead of adding $15.60 + $15.60 + $15.60 + $15.60 + $15.60 ...we'll multiply $15.60 by 5 .

Let's set up our multiplication expression: $15.60 x 5 . We'll stack the numbers one on top of the other.

It's a good habit to place the number that has the most digits on top . This makes the problem easier to solve.

Let's look at the number of digits in each number. 15.60 has four digits...

Let's look at the number of digits in each number. 15.60 has four digits...and 5 is one digit.

15.60 has more digits . This means we'll write 15.60 above the 5 .

Since we're multiplying this number, we'll write the times sign ( X ) to the left of the numbers.

Instead of an equals sign ( = ), we'll put a line underneath the number on bottom.

When writing a stacked multiplication expression with decimal numbers, the numbers should be lined up on the right .

Let's look at another example. We'll stack this expression: 4.5 x 38.12 .

First, let's look to see how many digits are in each number. 4.5 has two digits...

First, look to see how many digits are in each number. 4.5 has two digits...and 38.12 has four digits.

38.12 has more digits. This means we'll place 38.12 above 4.5 .

Then we'll make sure the digits to the right are lined up. The 2 is right above the 5 .

Solving multiplication problems with decimals

Multiplying decimal numbers is a lot like multiplying larger numbers . If you divide the large problem into a few smaller ones, it will be easier to solve. Let's see how this works by solving this problem: 2.3 x 4 .

Click through the slideshow to learn how to multiply decimals.

To solve our problem, we'll use a familiar tool: the times table .

When multiplying stacked numbers, start with the right digit on the bottom . The bottom number only has one digit: 4 .

We'll multiply 4 by the top number, 2.3 . Since there's no 2.3 in the times table, we'll have to multiply one digit at a time.

As usual, we'll solve the problem from right to left . So, we'll multiply 4 by the digit on the top right . Here, that's 3 .

Now it's time to solve 4 x 3 . We can use the times table .

4 x 3 is 12 , but there's no room to write both digits underneath the 4 and 3 .

Remember, this means we'll have to carry . We learned about carrying numbers in the lesson on multiplying larger numbers .

We'll write the right digit, 2 , under the line...

We'll write the right digit, 2 , under the line...then we'll carry the left digit, 1 , up to the next set of digits in the problem.

Now it's time for the next step. We'll multiply 4 x 2 .

4 x 2 = 8 . But we won't write 8 under the line yet. Remember, there's one more step.

We need to make sure we add the number we carried: 1 .

We'll set up our addition problem.

1 + 8 = 9 .

We'll write 9 beneath the line.

In our problem, we multiplied a decimal number: 2.3 . This means our answer will also need to be a decimal number.

Let's figure out where to put the decimal point ( . ).

In the problem, 2.3 has one digit to the right of the decimal point.

This means our answer will also have one digit to the right of the decimal point.

We'll place the decimal point so that only one digit is to the right : the 2 .

Our problem is solved. The total is 9.2 . We know that 2.3 x 4 = 9.2 . We can read this answer as nine and two-tenths .

Let's try another problem. This time we'll multiply money: $3.05 x 2 .

First, we'll multiply the bottom number, 2 , by the digit on the top right. That's 5 .

2 x 5 = 10 .

We'll write the 0 under the line...

We'll write the 0 under the line...and carry the 1 . We'll place it above the next digit.

The next digit is 0 .

Anything times zero is zero , so we know that 2 x 0 = 0 .

Remember, we need to make sure we add the 1 that we carried.

0 + 1 = 1 . We'll write 1 beneath the line.

Finally, we'll multiply 2 and 3 .

2 x 3 = 6 , so we'll write 6 beneath the line.

It's time to place our decimal point. We need to count the digits to the right of the decimal point in our problem.

3.05 has two digits to the right of the decimal point. They're 0 and 5 .

This means our answer will need to have two digits to the right of the decimal point.

We'll place the decimal point so that two digits are to the right: the 1 and the 0 .

Finally, we'll write a dollar sign ( $ ) to the left of the number.

We've solved the problem. $3.05 x 2 = $6.10 . We can read this as six dollars and ten cents .

Note : When determining where to place your decimal point in your answer, count the total number of digits to the right of each decimal point in your problem. For example, if you are simplifying 3.25 x 2.3, you would count the two digits in 3.25 plus the one digit in 2.3. Therefore, we should place the decimal point in our answer so that three digits are to the right (3.25 x 2.3 = 7.475).

Try solving these multiplication problems. Then, check your answer by typing it in the box.

Dividing decimals

Let's look at a different situation. Let's imagine you have a fence, and you want to plant 5 bushes in front of it. Your fence is 20 feet long. You'd like to space the bushes out equally, so you know you'll need to divide your fence into 5 equal sections. This means you'll need to divide 20 by 5 .

In the lesson on division , we learned how to set up division expressions. For the situation above, the expression would look like this:

In our expression, 20 is a whole number . But what if the length of the fence is a decimal number ? For instance, let's say it's 20.75 feet long. Believe it or not, dividing a decimal isn't that different.

When you set up an expression to divide a decimal number, it's important to make sure you're always dividing by a whole number . In our example above, 20.75 is being divided by the whole number 5 . Dividing by a whole number makes long division easier to manage.

Click through the slideshow below to learn how to set up division problems with decimals.

Let's set up this expression: 20.75 / 5 .

We learned in the lesson on division that dividing numbers is easier when the expression is written a little differently.

As usual, instead of writing the numbers side by side with a division symbol ...

As usual, instead of writing the numbers side by side with a division symbol ...we'll use the division bracket .

The number we're dividing goes under the division bracket. That's 20.75.

To the left of the division bracket, we'll write the number we're dividing by. In our problem, it's 5 .

Remember, the division bracket is also an equals sign .

The quotient , or answer, is written above it.

Let's set up another expression. This time, both numbers are decimal numbers: 80.1 / 4.2 .

First, we'll write the division bracket.

Next, we'll write the number being divided: 80.1 .

Finally, we'll write the number we're dividing by: 4.2 .

Since we're dividing a decimal number by a decimal number, there's one more step we need to do.

To make division easier, we'll change the the number we're dividing by into a whole number . This means we'll change 4.2 .

To make 4.2 a whole number, we'll need to move the decimal point so it comes after the last digit in the number.

This means we'll move it so it comes after the 2 .

Now all of the digits are to the left of the decimal point. We've created a whole number. 4.2 becomes 42 .

A whole number is usually written without a decimal point after it...

A whole number is usually written without a decimal point after it...so we'll drop the decimal point.

See how we did that? We moved the decimal point to the right and then dropped the decimal point.

Since we moved the decimal point in one number...

Since we moved the decimal point in one number...we'll also need to move the decimal point in the other number: 80.1 .

So we'll move this decimal point the same number of times .

80.1 becomes 801 .

801 is a whole number, so we'll drop the decimal point .

Now the division expression is 801 / 42 .

Moving decimals can be tricky, so it's important to change the number you're dividing by into a whole number first.

Let's try it one more time with a different expression: 0.4 / 0.02 .

First, we'll change 0 .02 into a whole number.

We'll move the decimal point one time to the right .

0.02 becomes 0.2 .

We still have a digit to the right of the decimal point: 2 . This means our decimal isn't a whole number yet.

So we'll move the decimal point to the right a second time.

0.2 becomes 2 . All of the digits are now to the left of the decimal point.

The zeroes and the decimal point are no longer needed. We'll drop them.

Since we moved the first decimal point two times to the right...

Since we moved the first decimal point two times to the right...we'll do the same to the second decimal point.

We'll move it one time...

We'll move it one time...then we'll add a zero ...

We'll move it one time...then we'll add a zero ...and then we'll move it a second time.

0.4 becomes 40 .

Since 40 is a whole number, we'll drop the zero and the decimal point.

The division expression is now 40 / 2 . Our problem is ready to be solved.

Dividing decimal numbers

In the previous slideshow, you practiced setting up division expressions with decimal numbers. Let's take a closer look at how to divide a decimal. Dividing a decimal number is a lot like dividing a whole number . There's just one extra step at the end.

Click through the slideshow to learn how to divide decimals.

We'll use long division to solve this problem: 6.5 / 2 .

We learned in the lesson on long division that when solving a long division problem, we'll follow a pattern until the problem is complete.

We'll begin with the left digit under the division bracket. This means we'll start with the 6 ...

We'll begin with the left digit under the division bracket. That means we'll start with the 6. ..and we'll figure out how many times it can be divided by 2 .

We'll use the times table to help us. Remember, if you need to review how to use the times table, you can revisit the lesson on multiplication . Now it's time to solve 6 / 2 .

6 / 2 = 3 .

We'll write 3 above the 6 .

Next, we'll multiply the 3 and 2 .

3 x 2 = 6 .

We'll write 6 below the 6 .

Next, we'll set up our subtraction problem.

6 - 6 = 0 . We'll write 0 below the line.

Now, we'll bring the 5 down and rewrite it next to the 0 .

05 means the same as 5 . 5 is large enough to be divided, so we'll figure out how many times 5 can be divided by 2 .

In the 2's column, we'll look for the number that's the closest to 5 but no larger than 5 . That's 4 .

4 is in the 2's row. That means 2 goes into 5 two times.

We'll write 2 above the 5 .

Now it's time to multiply the 2 and 2 .

2 x 2 = 4 .

We'll write 4 beneath the 5 .

Now it's time to set up our subtraction problem.

5 - 4 = 1 . We'll write 1 beneath the line.

Since our answer to the subtraction problem is 1 , we'll look under the bracket to see if there is another digit we can bring down.

There are no more digits for us to bring down. We learned in the long division lesson that we can write a zero next to the number under the division bracket.

So next to 6.5 we'll write 0 .

Now we can continue solving this problem. We'll bring the 0 down and rewrite it next to the 1 .

Let's see how many times 10 can be divided by 2 .

In the 2's column, we'll look for the number that's the closest to 10 but no larger than 10 . There's a 10 in the 2's column. That's exactly what we need!

10 is located in the 5's row. This means 2 goes into 10 five times.

We'll write 5 above the 0 .

Now it's time to multiply the 5 and 2 .

5 x 2 = 10 .

We'll write 10 beneath the 10 .

Next, we'll set up the subtraction problem.

Now it's time to solve. 10 - 10 = 0 .

Since the answer to the subtraction problem is 0 and there are no more digits to bring down, we're done dividing. There's just one last step we need to do.

In this problem, we divided a decimal number: 6.5 . This means our quotient , or answer, will have a decimal point.

We'll simply write a decimal point directly above the other decimal point. See where we put it between the 3 and 2 ?

We've completed the problem. The quotient is 3.25 . So 6.5 / 2 = 3.25 . We can read this as three and twenty-five-hundredths .

Find the quotient for each of the long division problems below. Check your answer by typing it in the box.

/en/decimals/converting-percentages-decimals-and-fractions/content/

Word Problems - Decimal Multiplication

Description:  This packet helps students practice solving word problems that require multiplication with decimals. Each page contains 6 problems. Each page also has a speed and accuracy guide to help students see how fast and how accurately they should be doing these problems. After doing all 12 problems, students should be more comfortable doing these problems and have a clear understanding of how to solve them. 

If a Cadillac car seats 6 people, how many people can fit into 12 Cadillacs? 

Practice problems require knowledge of how to multiply whole numbers and decimals.

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• Word Problems on Multiplication of Decimals

How to Solve Decimal Word Problems

Before learning about the multiplication of decimal numbers , sit back and think about where you saw decimals earlier. Have you seen it while buying your favourite candy? Probably! Have you seen it on the weighing scale while buying potatoes? Maybe! A decimal is a proper fraction whose denominator is a power of 10 . Such fractions are represented in the form of numbers, which can be identified by a (.) full stop in between the digits . Let’s learn about decimal numbers and the process of decimal multiplication.

Decimal Numbers

As said above, decimal numbers are numbers that have numbers like 10, 100, and 1000 in the denominator. Have a look below at the image.

Decimal number representation

Let’s learn how to perform the multiplication of such decimal numbers.

Rules to Solve Problems on Multiplication of Decimal Numbers

Solving decimal addition and subtraction is easy, as you do not have to change the decimal place. However, you have to change the place of the decimal when you perform multiplication or division on decimal numbers or numbers. Let’s understand decimal multiplication word problems with a practical example.

Suppose you went to buy your favourite candy, which costs Rs. 0.50 for one piece. You want to buy four candies. So how will you calculate the amount you have to pay the shopkeeper?

Four candies

So, you can calculate the amount by multiplication. You can see that the full stop, or period symbol, between 0 and 5 makes the number decimal. So here, you have to multiply. To perform decimal multiplication, you have to follow certain rules.

Here are the rules you must follow:

First, multiply the number by ignoring the decimal place.

The next step is to place the decimal point in the product after counting the number of digits before the decimal point in the multiplicand.

Let’s solve the candy problem by using these two rules.

The price of one piece = Rs. 0.50

The price of four pieces will be the price of one piece multiplied by 4, which is =$0.50 \times 4$.

First step of decimal multiplication

The next step is to place the decimal point by counting the number of digits before the decimal point in the multiplicand. Here, the multiplicand is 0.50. Hence, we place the decimal point by putting the decimal point after 0 in the product.

Note: Always start from the right side of the digits in the product.

There are two digits in front of the decimal point in the multiplicand. Hence, the result will be Rs. 2.00 as shown below.

Decimal placement after multiplication

So, this is how you can perform multiplication on decimal numbers.

Solved Examples of Decimal Multiplication

Find the product of 12.25 and 2.

Here, the multiplicand contains two digits after the decimal point. So in the solution, the product also has the decimal place after two digits from the right.

Determine the product of 14.3 and 4.

Find the product of 25.5 and 2.

Here, the multiplicand contains one digit after the decimal point. So, in the solution, the product also has the decimal place after one digit from the right.

Decimal Multiplication Worksheet

The questions in the decimal multiplication worksheet given below, along with the answers, will help you practice decimal multiplication much better.

• Find the product of 42.5 and 4

Ans:   170.00

• Find the product of 20.5 and 3

Ans:   61.50

• Find the product of 10.5 and 6

Ans:   63.00

• Find the product of 23.1 and 10

Ans:   231.00

In this article, you have learnt about decimal numbers. The uses of decimals in daily life and the rules that must be followed while performing decimal multiplication. You have learnt that when performing decimal multiplication, you must take care of the number of digits present in front of the decimal point. Apart from these, you have also learnt to solve decimal multiplication questions.

FAQs on Word Problems on Multiplication of Decimals

1. Can we multiply a decimal fraction with a decimal fraction?

Yes! We can multiply a decimal fraction by another decimal fraction. However, while writing the result, we have to consider the digits present before the decimal point in both the multiplicand and multiplier. Suppose the multiplicand has two digits in front of the decimal point, and the multiplier has one digit in front of the decimal point. Then the product will have three digits in front of the decimal point.

2. What happens if we place the decimal point by starting from the left?

If you start from the product's left side after multiplication, the answer you will get at the end will be wrong. Therefore, to avoid such mistakes, remember to start from the right while counting the digits to place the decimal points.

3. Why is it important to learn to solve word problems involving decimal multiplication?

It is important to learn decimal multiplication word problems because decimals appear when dealing with money, length, and weight. For example, while measuring your body weight, you must have noticed the numbers sometimes come in decimals. There are many examples of places where decimals are used. Therefore, decimal multiplications are necessary. In fact, all the arithmetic operations on decimal numbers are necessary.

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Mixed decimals word problems

Add, subtract and multiply decimals.

These grade 5 math word problems involve the addition, subtraction and multiplication of decimal numbers with one or two decimal digits . Some problems may have more than 2 terms, include superfluous data or require the conversion of fractions with denominators of 10 or 100.

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Decimal Multiplication Word Problems Worksheets for Kids

Printable Decimal Multiplication Word Problems Worksheets for Kids make learning fun! Help your child ace Decimal Multiplication Word Problems with our interactive worksheets. Download now for free!

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Multiply Decimal Numbers by 10, 100 or 1000: Summer Word Problems Worksheet

Summer-themed worksheet for students to practice multiplying decimal numbers by 10, 100, or 1,000.

Multiply Decimal Numbers by 10, 100 or 1000: Halloween Word Problems Worksheet

Halloween-themed worksheet for solving word problems on multiplying decimals by 10, 100 or 1,000.

Multiply Decimal Numbers by 10, 100 or 1000: Christmas Word Problems Worksheet

Engaging Christmas-themed worksheet to enhance students' skills in multiplying decimal numbers by 10, 100, or 1,000.

Multiply Decimal Numbers by 10, 100 or 1000: Shopping Word Problems Worksheet

Engaging worksheet with a shopping theme to practice multiplying decimal numbers by 10, 100 or 1,000.

Multiply Decimal Numbers by 10, 100 or 1000: Travel Word Problems Worksheet

Travel-themed worksheet that makes multiplying decimals by 10, 100, or 1,000 a fun expedition!

Multiply Decimal Numbers by 10, 100 or 1000: Sports Word Problems Worksheet

Sports-themed worksheet for mastering decimal multiplication by 10, 100, or 1,000 with word problems.

Multiply Decimal Numbers by 10, 100 or 1000: Cooking Word Problems Worksheet

Cooking-themed worksheet to practice multiplying decimal numbers by 10, 100 or 1,000!

Multiply Decimal Numbers by 10, 100 or 1000: Winter Word Problems Worksheet

Boost decimal multiplication skills with this winter-themed worksheet on multiplying by 10, 100, or 1,000.

Multiply Decimal Numbers by Whole Numbers: Summer Word Problems Worksheet

Summer-themed worksheet for students to practice multiplying decimal numbers by whole numbers.

Multiply Decimal Numbers by Whole Numbers: Halloween Word Problems Worksheet

Spooky-themed worksheet to enhance skills on multiplying decimals with whole numbers.

Multiply Decimal Numbers by Whole Numbers: Christmas Word Problems Worksheet

Enjoy a festive math worksheet, multiplying decimal numbers by whole numbers with a Christmas twist!

Multiply Decimal Numbers by Whole Numbers: Shopping Word Problems Worksheet

This worksheet lets students practice multiplying decimals by whole numbers through shopping-themed problems.

Multiply Decimal Numbers by Decimal Numbers: Shopping Word Problems Worksheet

Engaging worksheet that combines shopping theme with multiplying decimal numbers exercises.

Multiply Two Decimal Numbers with 1 Decimal Places: Shopping Word Problems Worksheet

Engaging worksheet on shopping-themed multiplication problems with 1-decimal place numbers.

Multiply Decimal Numbers with 2 Decimal Places by Decimal Numbers with 1 Decimal Place: Shopping Word Problems Worksheet

Solve shopping-themed problems by multiplying 2-place and 1-place decimal numbers in this worksheet.

Multiply Two Decimal Numbers with 2 Decimal Places: Shopping Word Problems Worksheet

Engaging worksheet for students to multiply two decimal numbers in a shopping-themed scenario.

Multiply Decimal Numbers by Whole Numbers: Travel Word Problems Worksheet

Travel-themed worksheet for solving word problems involving multiplication of decimals by whole numbers.

Multiply Decimal Numbers by Decimal Numbers: Travel Word Problems Worksheet

Travel-themed worksheet challenging students to solve word problems by multiplying decimal numbers.

Multiply Two Decimal Numbers with 1 Decimal Places: Travel Word Problems Worksheet

Engaging worksheet for students to practice multiplying two decimal numbers within travel-themed scenarios.

Multiply Decimal Numbers with 2 Decimal Places by Decimal Numbers with 1 Decimal Place: Travel Word Problems Worksheet

Travel-themed worksheet featuring word problems on multiplying 2-place and 1-place decimal numbers.

Multiply Two Decimal Numbers with 2 Decimal Places: Travel Word Problems Worksheet

Travel-themed worksheet for students to practice multiplying two decimal numbers with 2 decimal places.

Multiply Decimal Numbers by Whole Numbers: Cooking Word Problems Worksheet

Fun, cooking-themed worksheet for students to practice multiplying decimals with whole numbers!

Multiply Decimal Numbers by Decimal Numbers: Cooking Word Problems Worksheet

This worksheet involves solving word problems related to cooking that require multiplying decimal numbers.

Multiply Two Decimal Numbers with 1 Decimal Places: Cooking Word Problems Worksheet

Fun cooking-themed worksheet for practicing multiplication with two 1-decimal place numbers!

Multiply Decimal Numbers with 2 Decimal Places by Decimal Numbers with 1 Decimal Place: Cooking Word Problems Worksheet

Cooking-themed worksheet for mastering multiplication of 2-decimal and 1-decimal numbers.

Multiply Two Decimal Numbers with 2 Decimal Places: Cooking Word Problems Worksheet

Cooking-themed worksheet on multiplying two decimal numbers with 2 decimal places.

Multiply Decimal Numbers by Whole Numbers: Winter Word Problems Worksheet

Winter-themed worksheet to boost skills in multiplying decimals with whole numbers through word problems.

Multiply Decimal Numbers by Whole Numbers: Thanksgiving Word Problems Worksheet

Thanksgiving-themed worksheet to help students solve word problems involving multiplying decimals by whole numbers.

Your one stop solution for all grade learning needs.

Problems on Multiplication of Decimal Fractions

We will discuss here how to solve the word problems on multiplication of decimal fractions.

To multiply a decimal number:

(i) Perform the multiplication ignoring decimal point.

(ii) Place the decimal point in the product to get as many decimal places in the product as there are in the multiplicant.

Solved examples on word problems on multiplication of decimal fractions:

1.  Find the product of 12.2 and 4.

       12.2

         × 4

        48.8

Here the multiplicant contains one decimal place, so the product must contain one decimal place.

2. Price of 1 metre cloth is $ 49.75. Find the price of 16 metres of cloth.

Price of 1 metre cloth       =             49.75

Price of 15 metres of cloth =               × 6

                                                    29850

                                                     49750

                                                    796.00

Thus, price of 16 metres of cloth = $ 796

3. A train can run 45.8 km in one hour. What will be the distance travelled by the train in 5 hours?

Distance covered by train in 1 hour  =            45.8 km

Distance covered by train in 5 hours =            45.8

                                                                      × 5

                                                                    229.0

Therefore, in 5 hours train will travel 229 km.

4. 2.35 m of cloth is needed to make a shirt. How many metre of cloth is needed to make 10 such shirts?

Cloth needed for 1 shirt    =            2.35 m

Cloth needed for 10 shirts =            2.35

                                                     × 10

                                                      23.5

Therefore, 23.5 m of cloth is needed for 10 such shirts.

Decimal Place Value Chart.

Expanded form of Decimal Fractions.

Like Decimal Fractions.

Unlike Decimal Fraction.

Equivalent Decimal Fractions.

Changing Unlike to Like Decimal Fractions.

Ordering Decimals

Comparison of Decimal Fractions.

Conversion of a Decimal Fraction into a Fractional Number.

Conversion of Fractions to Decimals Numbers.

Addition of Decimal Fractions.

Problems on Addition of Decimal Fractions

Subtraction of Decimal Fractions.

Problems on Subtraction of Decimal Fractions

Multiplication of a Decimal Numbers.

Multiplication of a Decimal by a Decimal.

Properties of Multiplication of Decimal Numbers.

Division of a Decimal by a Whole Number.

Division of Decimal Fractions

Division of Decimal Fractions by Multiples.

Division of a Decimal by a Decimal.

Division of a whole number by a Decimal.

Conversion of fraction to Decimal Fraction.

Simplification in Decimals.

Word Problems on Decimal.

5th Grade Numbers

5th Grade Math Problems

From Problems on Multiplication of Decimal Fractions to HOME PAGE

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