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# How to Divide Decimal?

Dividing decimals is akin to whole number division, differing mainly due to the decimal point. A similar division approach (like we do for whole numbers) is followed for decimals in math. Before understanding the division of decimals, let’s recall what decimals and the meaning of decimal points are.

In Mathematics, decimals are specific types of numbers, with a whole number and the fractional part separated by a decimal point. The dot that exists between the whole number and fractions part is called the decimal point.

We can also perform various math operations on these numbers, including addition, subtraction, multiplication, and division.

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## What is the Division of Decimals?

Dividing Decimals is the same like dividing whole numbers, except for the way we handle the decimal point. There are different cases in dividing decimals, such as:

· Dividing Decimals by whole numbers
· Division of a Decimal Number by another Decimal Number
· Division of decimals by 10, 100 and 1000 ## Dividing Decimals by whole numbers

Let us understand this by an example Step 1: Begin by expressing the division problem in its standard form. Commence by dividing the whole number part by the divisor.

Step 2: Position the quotient’s decimal point directly above the dividend’s decimal point. Proceed by bringing down the tenth digit.

Step 3: Continue the division process, sequentially bringing down and dividing the remaining digits until the remainder reaches zero. This way, the decimal placement in the quotient corresponds to that in the dividend.

The stepwise procedure for dividing a decimal number by a whole number is given below for 1926 ÷ 4:

## Dividing Decimals by Decimals

Dividing decimals by another decimal involves converting the divisor into a whole number before proceeding with the division. Let’s explore the conditions and guidelines for this approach using an example.

Example: Let’s divide 48.65 ÷ 3.5

Solution: In this division scenario, both the dividend and the divisor are decimals. Therefore, we must convert the divisor into a whole number by following the steps below. Step 1: Given the dividend of 48.65 and the divisor of 3.5, our objective is to convert the divisor into a whole number. To achieve this, we multiply the divisor by 10, shifting its decimal point to the right, resulting in a whole number, 35.

Step 2: To maintain balance, we also multiply the dividend by 10, which transforms it into 486.5. Essentially, we shift both decimal points to the right until the divisor becomes a whole number.

Step 3: With 486.5 as the dividend and 35 as the divisor, we can now perform division as we normally would, resulting in a quotient of 13.9.

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## Solved Examples

Example 1: Find the quotient for 1.764 ÷ 0.012

Solution:

The given Divisor =0.012 and Dividend = 1.764

First, to simplify the division problem 1.764 ÷ 0.012, convert the divisor 0.012 into a whole number by shifting its decimal point three places to the right. Simultaneously, move the decimal point in the dividend three places to the right. It transforms the problem into 1764.0 ÷ 12.

So, 1.764 ÷ 0.012 = 1764.0 ÷ 12

The division is explained as shown in the diagram below

Thus, the quotient is 147.

Example 2: Calculate: 8.91 ÷ 2.2

Solution:

The given Divisor = 2.2 and Dividend = 8.91

To simplify the division problem with the divisor 2.2, you should convert it into a whole number by shifting its decimal point one place to the right. Similarly, move the decimal point in the dividend one place to the right to maintain the balance.

8.91 ÷ 2.2 = 89.10 ÷ 22

The division is explained as shown in the diagram below.

Thus, the quotient is 4.05.

## Essential Tips on Dividing Decimals

1. To simplify the division, convert the divisor into a whole number by multiplying the divisor and the dividend by the appropriate powers of 10.

2. If you need to divide a decimal number by 10, shift the decimal point to the left by one place. For instance, when dividing 45.67 ÷ 10, move the decimal point to the left, resulting in the answer 4.567.

3. When dividing a decimal number by 100, shift the decimal point to the left by two places. For example, for 324.6 ÷ 100, shift the decimal point two places to the left, yielding the answer 3.246.

4. If you’re dividing a decimal number by 1000, shift the decimal point to the left by three places. For instance, in the case of 8934.5 ÷ 1000, move the decimal point three places to the left, giving you the answer 8.9345.

## FAQs

#### How do you divide decimals step by step?

The stepwise procedure for dividing decimals by a whole number is given below:
Step 1: Write the given division expression in the standard form.
Step 2: Now, we have to divide the decimal number’s whole number part by the divisor.
Step 3: Place the decimal point in the quotient above the dividend’s decimal point and then bring down the tenths’ digit.
Step 4: If the divisor cannot divide the tenth digit of the obtained dividend, write 0 in the quotient and in front of the tenths’ digit. Otherwise, proceed with the division process.
Step 5: Repeat the above step and keep adding the zeroes in the dividend until 0 is obtained in the remainder.

#### Which way do you move the decimal point when dividing by 10?

Dividing a decimal by 10 moves the decimal point one place to the left.

#### How do you solve 5 divided by 100?

Dividing 5 by 100 involves only placing the decimal point in the numerator, such as 5/100 = 0.05. That means the decimal point will shift to the left by two places since 100 has two 0’s.

#### What is 31 over 100 as a decimal?

31 over 100 can be written as 31/100. Here, the denominator contains two 0’s. Hence, we have to place the decimal point after two digits, such as 0.31.

#### How do you divide a decimal by 10?

When we divide a decimal number by 10, the decimal point will shift to the left by one place since 10 has only one zero over 1. Gloria Mathew writes on math topics for K-12. A trained writer and communicator, she makes math accessible and understandable to students at all levels. Her ability to explain complex math concepts with easy to understand examples helps students master math. LinkedIn

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