We can divide decimals just like we do for whole numbers, except for the special consideration of the decimal point. When we divide decimals, we have to change the divisor and the dividend to a whole number. We can do this by moving the decimal point to the right for the divisor and then moving the decimal point of the dividend for the same number of places to the right. The resultant numbers can be divided as we do regular divisions.

Here’s what we’ll cover:

- What are decimals?
- Division of decimals
- How do you divide a whole number by a decimal?
- How to divide a decimal by a whole number?
- How do you divide a decimal number by another decimal?
- Dividing decimals using the long division
- Solved Problems
- Practice Problems

## What are Decimals?

Decimals constitute the extended number system wherein we can express tenths, hundredths, thousandths, and so on. Although it may seem a bit complicated working with decimals, it is quite similar to whole number operations. A decimal number consists of a whole number part and the fractional part. A dot separates the two parts. The numbers after the decimal point represent a value smaller than one.

For example, 27.15 is a decimal number, 27 is its number part, and 15 is the decimal part. This number can be expanded as follows: 27.15= 20 +7 + 0.1 + 0.05.

Is a decimal a whole number? A decimal number cannot be a whole number, as any number to the right of a decimal point has a value less than 1. On the other hand, a whole number can always be written as a whole number. For example, 6, 12, 23 can be written as decimal numbers such as 6.0, 12.0, 23.0. |

### Division of Decimals

The division of decimals is similar to the normal division process. However, we must pay special attention to the decimal point and place it correctly in the quotient. The following postulates will help understand the process of division of decimals.

### How Do You Divide A Whole Number By A Decimal?

- To divide a whole number by a decimal, say 41.2 , we will write the whole number as a decimal.
- Here the whole number is 4. As 1.2 has one place to the right of the decimal point, we can rewrite 4 as 4.0. Now, our problem is 4.0 ÷ 1.2. Note: You cannot add zeros to the left of the decimal point. 4 can be written as 4.0 or 4.00, but not as 40 or 400.
- Now, we will shift the decimal points to the right until we have whole numbers. We have to move them by the same amount for each number. So, 4.0 ÷ 1.2 into whole numbers will be 4.0 becomes 40, and 1.2 becomes 12. Now, the problem is 40 ÷ 12.
- Next, we will solve this using the long division method. We will add a decimal to extend the dividend if we have reached the end of the answer line and there is a remainder left to divide. We will add a decimal point followed by a 0.

### How to Divide A Decimal by A Whole Number?

We can divide a decimal number by a whole number as follows:

- Firstly, divide the two numbers normally, i.e., ignoring the decimal point.
- Then, place the decimal point in the quotient as it is placed in the same dividend.
- For example, 28.2 ÷ 2 = 14.1

### How Do You Divide A Decimal Number By Another Decimal?

We can divide a decimal number by a decimal number as follows:

- Firstly, multiply the divisor by as many tens as necessary until we get a whole number
- Then, multiply the dividend by the same number of tens.
- For example, 18.6 ÷ 0.6 becomes 186 ÷ 6 on removing the decimal, and the answer will be 31.

When the dividend has the decimal place more than the divisor’s decimal place:

- Divide normally while ignoring the decimal until you get zero as the remainder. For example, we have to divide: 0.06 ÷ 0.3. We will ignore the decimals and divide them as 6 ÷ 3 = 3.
- Now we will place the decimal point by the following formula:
- Dividend’s decimal place – Divisor’s decimal place= Quotient’s decimal place. So, using the formula, we get 2-1 =1. Hence, the quotient will have a decimal before a number, i.e., 0.3

When the dividend has the decimal place less than the divisor’s decimal place:

- We will first convert the decimal to a fraction. For example, 0.8 ÷ 0.02 can be written as

How is the multiplication of decimals different from the division of decimals?Both the multiplication and division process involves shifting the decimal places in the answer. In multiplication, the decimal places are added to the resultant answer. Contrastingly, the number of decimal places is subtracted in the solution when you divide by a decimal. For example, 0.0030 × 0.005 = 0.000015, and 0.0030 ÷ 0.005 = 0.6. Thus, we can observe that the division and multiplication processes are the same as the normal division or multiplication. The only difference arises in terms of the decimal positions, which are added in multiplication but subtracted in the division. |

#### How To Divide Decimals using the Long Division

We can easily divide by a decimal using the long division method, just like we do for the normal long division. The following steps explain the process of the long division of decimals.

- Firstly, write the numbers to be divided as per the standard form. Now, divide the whole number part by the divisor.
- Next, place the decimal point in the quotient exactly above the decimal point of the dividend. Now, bring down the tenth digit.
- Next, we will bring down the other digit in sequence and divide until we get zero as the remainder.
- So, the decimal in the quotient is similar in terms of position to the decimal in the dividend.

The following tips will help you solve problems wherein you have to divide by a decimal.

- Multiplying by the powers of 10 will convert the divisor to a whole number. You must also multiply the dividend number by the same powers of 10.
- If you have to divide a decimal number by 10, shift the decimal point by one place to the left.
- If you have to divide a decimal number by 100, shift the decimal point by two places to the left.
- If you have to divide a decimal number by 1000, then shift the decimal point by three places to the left.

#### Solved Examples

**Example 1: Emma has a collection of chocolates that weigh 0.8 grams each. How many chocolates does she have if their total weight is 376 grams?**

**Solution: **Given: The weight of one chocolate is equal to 0.8 grams.

The total weight of all the chocolates is equal to 376 grams.

We can find the number of chocolates by dividing the total weight by the weight of one chocolate.

= 376 ÷ 0.8

= 376 ÷ 8/10

= 376 × 10/8

= 3760/8

= 470

Emma has 470 chocolates in total.

**Example 2: There are a few bags of wheat each weighing 97.5 kg. Given the total weight of all the bags is 487.5 kg. Find the total number of bags of wheat.**

**Solution: **Total weight of all the bags = 487.5

Each bag weighs = 97.5

Total number of bags = Total weight of all bags ÷ weight of each bag

So, 487.5 ÷ 97.5

The required number of bags of wheat are 5.

**Example 3:** **John used 465.6 kg of potatoes to make 5 batches of chips. How many kilograms of potatoes did he use in one batch?**

**Solution:** We can calculate the quantity of potatoes that John used in one batch by dividing the total quantity of potatoes by the number of batches i.e., 465.6 ÷ 5.

Practice ProblemsQuestion 1: Solve the following questionsa. 23.5÷1.2 b. 141.32÷2.2 c. 89.5÷5 d. 22.1÷1.4 Question 2: Riya has $676.30. She uses $45 to buy a book. If she has to distribute the remaining amount amongst 5 people, what will be the share of each member?Question 3: The product of 2 decimal numbers is 114. If one of them is 45.6 then what is the other number?Question 4: The cost of 11 pens is $ 48.10. What is the cost of 1 pen?Question 5: How would you divide $1134.8 amongst 32 people equally? Calculate the share of each person. |