# Multiplying & Dividing Decimals : Concept, Practice & Rules

## Multiplying and Dividing Decimals

**Multiplying and dividing decimals** is similar to multiplying and dividing whole numbers with one small difference: *decimal placement*, which is the place value in a number where the decimal is. For both multiplication and division, there is a strategy to place the decimal that adds one simple step to the process.

For multiplication, that extra step is placing the decimal the *same number of places* as the decimal placements in all factors combined. Because of this, the decimal placement can be determined before calculating the answer. If we have one factor with two decimal places and another with one, our answer will have three decimal places.

Example: 3.8 x .007. 38 x 7 is 266. 3.8 has one decimal place and 0.007 has three, giving us four total. Since 266 only has three decimal placements available, we will need to add a zero as the fourth. Therefore, 3.8 x 0.007 = 0.0266.

Division is similar, only we move the decimal placements *before* the calculation. Decimal placements are removed until the number we are dividing by (the *divisor*) is a whole number. Then, we use the same decimal place of the number into which we are dividing (the dividend) for our answer.

Example: 50.22 / 3.1. 3.1 is a decimal, so we'll move everything over one decimal place to make it a whole number. This gives us 502.2 / 31. Without any decimal, our answer is 162. Since 502.2 has one decimal place, so will our answer. 50.22 / 3.1 = 16.2.

## Multiplying Decimals

**Decimal numbers**, those numbers with a decimal point in them, aren't scary or difficult to work with if you know the shortcuts that I will show you. In this video, we are specifically talking about multiplication and division of decimal numbers. I will show you that multiplying and dividing decimal numbers is exactly the same as multiplying and dividing whole numbers with just one difference.

In the real world, multiplying and dividing decimals happens all the time, so being able to multiply and divide decimals is an essential skill to have. For example, when you are shopping, you may need to quickly find out how much tax you can expect to pay for your purchase so that you can keep an eye out so you are not overcharged.

Let's first look at multiplying decimal numbers. Let's say we want to multiply 1.25 and 3.5. What do we do? We proceed by first multiplying the two numbers while ignoring the decimal. So we go ahead and multiply 125 with 35. We get 4,375.

Now this is where the one difference comes in and where we can apply our trick. The trick here is to count the number of decimal places we have in total. We have two from 1.25 and we have one from 3.5. We have a total of three decimal places, so that tells us that we need to count three decimal places, and that is where we put our decimal point. So our decimal goes between the 4 and the 3. Our final answer is 4.375.

## Multiplying Decimals from Word Problems

The most common use of multiplying decimals, outside of statistics and advanced mathematics, is calculating money. Tax, interest, dividends, and even everyday prices use decimals. In United States currency, dollars are whole numbers and cents are decimals. Multiplying one price by another involves multiplying decimals.

Example: Maia lost her job and deferred her student loans for one year. She owes $59,847.19 with an interest rate of 5.875% (0.05875). How much interest will be added by the end of her deferment?

The equation we need to solve here is 59,847.19 x .05875. Using our strategy for multiplying decimals, we will first multiply the numbers without decimals. 59,84719 x 5875 is 35,160,224,125. Then we add the decimal places. $59,847.19 has two decimal places and .05875 has five. This gives us seven decimal places for our answer. 59,847.19 x .05875 = 3,516.0224125. Rounded to the hundredths place for cents, Maia's added interest will be $3,156.02.

## Dividing Decimals from Word Problems

Dividing decimals typically occurs when we have to split a decimal amount by another decimal amount. It can apply to money, distance, time, food; anything that can be divided can also be divided again.

Example: Trey made chili for his big game night. After everyone has had their fill, there are 12.5 cups left in his crockpot. How many 2.5 cup containers can he fill for leftovers?

This equation is 12.5 / 2.5. Our strategy tells us to move the decimal until both numbers are whole. Since 12.5 and 2.5 both have one decimal place, we end up with 125 / 25, which is 5. Trey will have 5 containers of leftovers.

## Multiplying and Dividing Decimals Practice

#### Example One: 4.5 x 9.72

First, multiply the factors without decimals. 45 x 972 = 43,740. Next, count the number of decimal places in both factors. 4.5 has one and 9.72 has two, making three total. Finally, give our previous answer a decimal point three places in. 4.5 x 9.72 = 43.74.

#### Example Two: 1.44 / 0.072.

For this problem, all we have to do is move the decimal points until the second number is a whole number. 1440 / 72 = 20. Therefore, 1.44 / 0.072 = 20.

#### Example Three: Kei makes $10.25 an hour. If he works 36.7 hours in one week, how much did he earn before taxes?

The equation for this word problem is $10.25 x 36.7. Multiplying without decimals gives us 1025 x 367, which is 376,175. 10.25 has two decimal places and 36.7 has one, giving us three total. So, $10.25 x 36.7 = $376.175, rounded up to $375.18 for a dollar amount.

#### Example Four: Cortney drives 231.42 miles with her cruise control set at 55.1 mph. For how many hours was she driving?

Here we want to divide 231.42 by 55.1. Making the second number whole leaves us with a decimal place remaining in the first number. This means our answer will have one decimal place too. 2314.2 / 551 = 4.2, which is the same as 231.42 / 55.1. Cortney drove for 4.2 hours.

## Lesson Summary

In this lesson, we covered **multiplying and dividing decimals**, or numbers with values to the right of the decimal point. There is a strategy for each that makes a complicated process much simpler. For multiplication, multiply the numbers without the decimal places, then use the total number of decimal places from the sum of both factors for the answer. For division, move the decimal places on both numbers until the divisor is a whole number, then divide like usual. The decimal place of the answer will be the same as the dividend.

For word problems, it is important to use the context to determine what operation needs to be performed. Between multiplication and division, the key word to look for is *total*. If the total amount of something is expressed, the problem will likely be division. Likewise, if the total needs to be found, it's probably multiplication.

## Sales Tax: A Multiplication Example

Now let's look at a real-world example. You are shopping, and you want to buy two pairs of shoes. The total for the two shoes is $62.18. The sales tax in your area is 6 percent. How much should you expect to pay in sales tax?

To solve this problem, you need to multiply your total of $62.18 with the sales tax of 0.06 percent. Yes, we are multiplying the two decimals together. Remember what we just learned? First, go ahead and multiply as if there are no decimals. We multiply 6,218 with 6 to get 37,308. Then we count the total number of decimal places we have between our two numbers. We have four.

Now we count four decimal places in our answer to find where we should put our decimal point. We place it between the beginning 3 and the 7. Our final answer is 3.7308. We can expect to pay around $3.73 in sales tax.

## Dividing Decimals

Let's move onto division now. Division is also similar to dividing whole numbers. The only difference here is that if the number we are dividing by is a decimal, then we will want to convert it to a whole number before we divide. If we are dividing 7.24 by 0.2, we would first change the 0.2 to a 2. To do that, we move the decimal place over one space to the right.

Because we are doing this to one number, we also need to move the decimal place one place to the right in the other number. So my 7.24 becomes 72.4. Now we can go ahead with our long division of 72.4 divided by 2. Once we get our answer, we write in the decimal point so that it matches the position of the decimal point in the 72.4

Our answer is 36.2. See how the decimal point in the answer is directly above the decimal point in 72.4?

## Sharing Burgers: A Division Example

In the real world, we come across division problems also. For example, we could be eating out with three of our friends at a burger place. Once the check comes, we need to figure out how much everyone should pay since we all shared the food. If the total of the check is $36.12 and there are four people total, how much should each person pay?

To answer this question, we need to divide $36.12 by 4. The number we are dividing by is already a whole number, so we don't need to convert it or move any decimal points around. We go ahead and we do the long division for 36.12 divided by 4. My answer is 9.03. Notice again how the decimal points are aligned.

## Lesson Summary

We've now covered both multiplication and division of decimal numbers. Let's review what we've learned. We know that our **decimal numbers** are the numbers with decimal points in them. To multiply them, we go ahead and multiply as if there were no decimals. Then we count the number of decimal places between our numbers to find the number of decimal places we need in our answer. To divide, we first convert the number we are dividing by to a whole number if it is a decimal number.

If it is already a whole number, then we can go ahead and perform long division with our problem. If we needed to convert the number we are dividing by to a whole number by moving the decimal point over a certain number of places, then we also need to move the decimal point the same number of places over in the other number. After performing the long division, we put the decimal point in our answer so that it is aligned with the decimal point underneath.

## Learning Outcome

Once you are finished reviewing this lesson you should be able to solve a multiplication or division problem that includes decimals.

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## Multiplying Decimals

**Decimal numbers**, those numbers with a decimal point in them, aren't scary or difficult to work with if you know the shortcuts that I will show you. In this video, we are specifically talking about multiplication and division of decimal numbers. I will show you that multiplying and dividing decimal numbers is exactly the same as multiplying and dividing whole numbers with just one difference.

In the real world, multiplying and dividing decimals happens all the time, so being able to multiply and divide decimals is an essential skill to have. For example, when you are shopping, you may need to quickly find out how much tax you can expect to pay for your purchase so that you can keep an eye out so you are not overcharged.

Let's first look at multiplying decimal numbers. Let's say we want to multiply 1.25 and 3.5. What do we do? We proceed by first multiplying the two numbers while ignoring the decimal. So we go ahead and multiply 125 with 35. We get 4,375.

Now this is where the one difference comes in and where we can apply our trick. The trick here is to count the number of decimal places we have in total. We have two from 1.25 and we have one from 3.5. We have a total of three decimal places, so that tells us that we need to count three decimal places, and that is where we put our decimal point. So our decimal goes between the 4 and the 3. Our final answer is 4.375.

## Sales Tax: A Multiplication Example

Now let's look at a real-world example. You are shopping, and you want to buy two pairs of shoes. The total for the two shoes is $62.18. The sales tax in your area is 6 percent. How much should you expect to pay in sales tax?

To solve this problem, you need to multiply your total of $62.18 with the sales tax of 0.06 percent. Yes, we are multiplying the two decimals together. Remember what we just learned? First, go ahead and multiply as if there are no decimals. We multiply 6,218 with 6 to get 37,308. Then we count the total number of decimal places we have between our two numbers. We have four.

Now we count four decimal places in our answer to find where we should put our decimal point. We place it between the beginning 3 and the 7. Our final answer is 3.7308. We can expect to pay around $3.73 in sales tax.

## Dividing Decimals

Let's move onto division now. Division is also similar to dividing whole numbers. The only difference here is that if the number we are dividing by is a decimal, then we will want to convert it to a whole number before we divide. If we are dividing 7.24 by 0.2, we would first change the 0.2 to a 2. To do that, we move the decimal place over one space to the right.

Because we are doing this to one number, we also need to move the decimal place one place to the right in the other number. So my 7.24 becomes 72.4. Now we can go ahead with our long division of 72.4 divided by 2. Once we get our answer, we write in the decimal point so that it matches the position of the decimal point in the 72.4

Our answer is 36.2. See how the decimal point in the answer is directly above the decimal point in 72.4?

## Sharing Burgers: A Division Example

In the real world, we come across division problems also. For example, we could be eating out with three of our friends at a burger place. Once the check comes, we need to figure out how much everyone should pay since we all shared the food. If the total of the check is $36.12 and there are four people total, how much should each person pay?

To answer this question, we need to divide $36.12 by 4. The number we are dividing by is already a whole number, so we don't need to convert it or move any decimal points around. We go ahead and we do the long division for 36.12 divided by 4. My answer is 9.03. Notice again how the decimal points are aligned.

## Lesson Summary

We've now covered both multiplication and division of decimal numbers. Let's review what we've learned. We know that our **decimal numbers** are the numbers with decimal points in them. To multiply them, we go ahead and multiply as if there were no decimals. Then we count the number of decimal places between our numbers to find the number of decimal places we need in our answer. To divide, we first convert the number we are dividing by to a whole number if it is a decimal number.

If it is already a whole number, then we can go ahead and perform long division with our problem. If we needed to convert the number we are dividing by to a whole number by moving the decimal point over a certain number of places, then we also need to move the decimal point the same number of places over in the other number. After performing the long division, we put the decimal point in our answer so that it is aligned with the decimal point underneath.

## Learning Outcome

Once you are finished reviewing this lesson you should be able to solve a multiplication or division problem that includes decimals.

To unlock this lesson you must be a Study.com Member.

Create your account

#### What is an example of a decimal word problem?

The laptop KC wants is $809.97. Their state tax is 6%, or $1.06 times the sale price. How much should KC expect to spend total?

The equation here is $809.97 x $1.06. The strategy for multiplying decimals tells us to multiply without decimals, so 80997 x 106 = 8,585,682. Next, we add the number of decimal places in the factors. Both 809.97 and 1.06 have two decimal places, giving us four total. Then, we move the decimal point four places in on our previous product. 809.97 x 1.06 = 858.5682. KC can expect to spend $858.57 on their new laptop.

#### How do you divide decimals in word problems?

First, change the decimal placement in both numbers so that the divisor is a whole number. Then, divide like usual. The decimal place in the dividend will be the same in the answer.

#### How do you solve word problems involving multiplying decimals?

First, determine the equation using the numbers and context provided in the problem. Then, multiply the factors without decimal points. Next, add the decimal places of all factors together. Finally, move the decimal point on the previous answer the same number of spaces as the added total.

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