Dividing Decimals Definitions & Examples

Introduction

Dividing decimals is a math skill that you will likely need at some point in your life, whether you are dealing with personal finances or working in a profession that requires mathematical skills. While the concept of dividing decimals may seem daunting at first, it is actually not difficult once you understand the basics. In this blog post, we will provide a definition for dividing decimals, as well as some examples to help illustrate the concept.

What is a Decimal?

A decimal is a number that expresses a fractional value. It has a point or decimal marker to the left of the units place. The numbers to the right of the decimal marker represent tenths, hundredths, thousandths, etc. For example, the number 12.345 has a 5 in the thousandths place, indicating 5/1000 or 1/200.

How to Divide Decimals?

When you divide decimals, the process is very similar to division with whole numbers. The only difference is that you need to be careful of the decimal places. In order to divide decimals, follow these steps:

1) line up the decimal points in the dividend and divisor
2) begin dividing as usual, but keep track of the decimal places in both the dividend and divisor. The number of decimal places in the answer will be equal to the number of decimal places in the dividend
3) once you have your answer, count the number of digits to the right of the decimal point in both the dividend and divisor. This will be the same number of digits that need to go after the decimal point in your answer.

For example, let’s say we want to divide 7.56 by 3:

7.56 ÷ 3
We line up our numbers like this:

3|7.56
——-
2.52 (we bring down a 0 from 7.56 since there’s nothing else to bring down)
3|2.52
——-
.84 (notice how there are two digits after the decimal point in both 7.56 and 3, so there will be two digits after the decimal point in our final answer as well)

Dividing Decimals by Whole Numbers

To divide a decimal by a whole number, we first need to understand what a decimal is. A decimal is simply a number that has a point after it denoting the fraction of that number. For example, 3.14 is 3 and 14/100, or three hundred fourteen thousandths.

Now that we know what a decimal is, let’s look at an example of how to divide decimals by whole numbers. Let’s say we want to divide 3.14 by 2. To do this, we would first write out our problem like this:

3.14 ÷ 2 =

Since 2 is a whole number, we can simply divide 3 by 2 to get 1.5 as our answer. However, if we want to be more precise, we can rewrite our problem as follows:

3.14 ÷ 2 = 1.57

In this case, we are showing that our answer has two decimal places after the point since 3.14 has two decimal places after the point as well.

Long Division of Decimals

To divide a decimal by a whole number, you can use long division. This is the same process you would use to divide any number, but because decimals are involved, there are a few things to keep in mind. Here’s an example:

Say we want to divide 3.4 by 2. To set this up in long division, we would write:

3.4
2 ) 6.8 (this is called the dividend)

To figure out the first digit of the answer, we divide 2 into 3. The answer is 1 with a remainder of 1, so we write “1” above the line and bring down the next decimal digit, which gives us 11 (the 1 from before plus the 4). We continue dividing:

3.4
2 ) 6.8
11
2 ) 22
20
2
0
The final answer is 1.32

Dividing Decimals by Decimals

To divide one decimal by another, follow these steps:

1. Change the division problem to an equivalent multiplication problem by multiplying both the dividend and divisor by a power of 10 so that both numbers are whole numbers.
2. Divide as you would with any whole number division problem, and
3. count the number of digits to the right of the decimal point in the original division problem—this will be the number of zeroes you need to add to the end of your answer as a place holder.
If you are dividing a decimal by a non-decimal, see our page Dividing Decimals by Whole Numbers.

Here is an example: What is 0.4 ÷ 0.2?

First, change this to an equivalent multiplication problem: 0.4 ÷ 0.2 = 0.4 × 5 = 2

Now we can divide as usual, 2 ÷ 5 = 0 remainder 2, so our answer is: 0.40

What is Dividing Decimals?

When you divide decimals, the process is very similar to division with whole numbers. The only difference is that you have to keep track of the decimal places. In order to divide decimals, follow these steps:

1. Line up the decimal points in the two numbers.
2. Divide as you would with whole numbers, keeping track of the decimal point.
3. Place the decimal point in the answer directly above the decimal point in the dividend.

Let’s look at an example: What is 7.06 divided by 2?

First, we line up the numbers on either side of the division sign, making sure that the decimal points are lined up:

7.06
÷ 2

Then, we divide as normal, starting at the ones column and moving left:

70.6
÷ 2
—
1 (2 goes into 6 three times) 3 times 2 is 6 so we put a 3 above where we found a 6 70-12=58 58÷2=29 29 goes into 5 two times with a remainder of 1 2 times 2 is 4 plus 1 more is 5 so we put a 5 above where we found a 5 29-10=19 19÷2=9 9 goes into 1 zero times with a remainder of 1 0 times 2

Examples of Dividing Decimals

Dividing decimals is a fundamental math skill that students must learn in order to be successful in mathematics. There are a variety of ways to divide decimals, but the most common method is to use long division. This process can be difficult for some students, so it is important to provide plenty of practice opportunities.

One way to provide practice is to give students a list of decimal numbers and have them divide them using long division. Another approach is to use word problems that require students to divide decimals in order to solve the problem. Either way, it is important that students understand the concept behind dividing decimals before they try to complete any problems.

The following are some examples of dividing decimals:

16.4 divided by 4 = 4.1
7.6 divided by 3 = 2.5
12 divided by 5 = 2.4

Conclusion

Dividing decimals can be a tricky concept for students to grasp, but it is a critical math skill. By using the tips and tricks in this article, you can help your students master decimal division in no time. And as always, if you have any questions or would like additional resources, please feel free to reach out to us. We’re here to help!