How to Divide Decimals By Decimals

Do you get confused about where to place a point when dividing decimals by decimals? Many students find decimal division tricky at first, but once they understand the rule of shifting the decimal point, it becomes easier and simpler. 

To divide a decimal by a decimal, move the decimal point to the right in both the divisor and dividend and simply divide it.

In this guide, you will learn how to divide decimals by decimals, fractions, or powers of 10 step by step with all easy examples and explanations.

How to Divide Decimals by Decimals

A Decimal is a way to represent numbers that are not whole numbers; it represents a part of a whole using the decimal point (.) to separate the whole number from the fractional part.

For Example 

5.6

In these values, 5 is a whole number, and  .6 is the decimal part.

Steps to Divide decimals by decimals 

When you divide a decimal by another decimal, the main point behind it is to make the divisor a whole number. Steps to divide decimals by decimals are : 

• Step 01 : 

Move a decimal point to the right in  both numbers until the divisor becomes a whole number 

• Step 02 : 

Multiplying both numbers by 10,100, or 1000, depending on how many decimal places there are. Simply divide the numbers.

• Step 03 :

Now place the decimal in your answer. 

Example ;

Solution

The answer is  4

How to Divide a Whole Number by a Decimal

When dividing a number or integers by a decimal, make the divisor a whole number first. You need to place a decimal point to the right to make it a whole number and move the exact number of places in the dividend. Then simply divide it. 

• Let's take an example for better understanding. 

• Steps 01:

The divisor 0.4 moves the decimal one place to the right to make it 4.

• Step 02:

When you move the decimal in the divisor, you must move the exact number of places in the dividend. 

• Step 03:

 0.4 becomes 4, and 8 becomes 80. Now divide it 

The answer is 20 

Example 02

• Step 01:

In 0.05, move the decimal two places right to make it 5.

• Step 02 : 

Move the decimal in 15, then 15 becomes 1500

• Step 03 : 

Now simply divide the values 1500 ÷ 5

How to Divide a Decimal Number by a Whole Number

If you want to know how to divide a decimal number by a whole number, or use long division. You just need to ignore the decimal and simply divide it, then count where the decimal was in the value. So, place the decimal in your answer at the same position.

Let’s take an Example. 

Solution 

• Step 1 : 

Just ignore the decimal and divide the 48 by 6

Step 02 : 

Now count the decimal where the decimal was in 4.8, so place it in your answer at the same position.

So answer =0.8 

Get Guidance from our math experts for more explanation and examples. 

Divide a decimal by Decimals using long division  

You cannot directly divide a decimal by a decimal; it's a little bit complicated. You need to move the decimal point from the divisor to make it a whole number, also remove the decimal from the dividend, then simply divide the values.

Step 01: Move the decimal point  

To make a divisor a whole number, move its decimal one place to the right, 0.2 to 2

Now remove the decimal in the dividend (0.84), the same number of places, it becomes 0.84 to 8.4

Step 02: Using the long division method

The answer is 4.2

How to Divide a Decimal without a Calculator 

Dividing decimals might look tricky, but once you understand where to move the decimal point, it's very easy.

Let’s take an example

Solution 

Step 01: 

The divisor is 0.8. To make it a whole number, move the decimal one place to the right in  both numbers 

Step 02: 

Now simply divide it.

The answer is 8

How to Divide a Decimal by a Fraction

When you divide a decimal by a fraction, you can simply turn the problem into multiplication by flipping the fraction.

Example 01 

• Step 01: Keep, Change, Flip rule 

In this rule, you keep the first number (decimal value). Change the division sign into multiplication and flip the fraction.  

Solution

• Step 02: Multiply the values 

 $$=0.8 \times 2$$

Example 02 

Solution 

Step 01: Keep the first values, change the divide sign into multiplication, and flip the fraction

Step 02: Multiply 2.4 by 3, which is 7.2, so,

=7.22

Step 03: Divide the values 

The answer is 3.6

How to Divide a Fraction by a Decimal

To convert the decimal value into a fraction, change the division into multiplication, and flip the second fraction. Then, multiply the fractions and simplify the result. Steps are:

Example: 01

Step 01: Convert the Decimal to a fraction 

To convert the decimal into a fraction. Place 1 under the point of 0.5 and place zeros according to decimal values, and simplify. 

Now values become:

Step 02: Apply the keep, change, and flip rule 

Keep the first value, change the division signs into multiplication, and flip the fraction.

Step 03: Multiply the values and simplify them 

Example 02

The answer is 3.75 

Also, learn about comparing fractions 

How to Multiply and Divide Decimals by Powers of 10 

To multiply a decimal, just move the point to the right, and for division, move the point to the left. Powers of 10 are numbers such as: 10,1000,1000,10,000, etc. Each number has zero added, then it becomes

There are rules to solve the decimals with the power of 10. 

• If you multiply decimals by a power of 10, then you have to move the point to the right by as many zeroes as there are.
• If you are dividing a decimal by a power of 10. Then move the decimal point to the left by as many zeros as there are.

How to Multiply a Decimal by Powers of 10

When you multiply a decimal by 10,100,100, etc. You just have to move the point to the right as many zeros as there are.

Multiply by 10

If you want to multiply by 10, then move the decimal one place right because 10 has one zero, so the decimal moves one place right 

Multiply  by 100

If you want to multiply by 100, then move the decimal two places right because 100 has one zero, so the decimal moves two places right.

Multiply by 1000

If you want to multiply by 1000, then move the decimal three places right because 1000 has three zeros, so the decimal moves three places right 

How to Divide Decimals by Powers of 10 

When you are dividing by 10,100, or 1000, you just have to move the decimal point; no need for actual dividing. There is a rule that says:

•  You have to move the decimal point to the left.
• The number of places you move =the number of zeros.

Remember this rule and solve the problem.

Divide by 10

If you want to divide a decimal by 10, then you move the decimal one place left because 10 has one zero, so the decimal moves one place left.

Example 01

 Move the decimal one place to the left, and then it becomes 

Example 02 

Move the decimal one place to the left. 

Divide by 100

If you want to divide a decimal by 10, then you move the decimal two places left because 100 has two zeros, so the decimal moves two places left.

Example 01 

Example 02

Divide by 1000

If you want to divide a decimal by 1000, then you move the decimal three places left because 1000 has three zeros, so the decimal moves three places left.

Example 01

Example 02 

Conclusions 

Decimals are the values that are represented in points. To solve Decimal values, you need to understand the rules of shifting the points, and then it becomes so easy. In our blog, we addressed all queries related to decimals with examples, which helps you in learning decimals. With practice, you will get faster and more confident at solving any decimal division problem.