The method of dividing the decimal numbers is the same as the division of whole numbers. So, the 5th grade math students who want to divide the decimal numbers either by decimal or whole numbers must know the properties of the division of decimal numbers. This will article will support you to learn in detail about the properties of the division of decimal numbers with examples.

**Do Refer:**

## What is a decimal?

A decimal number is an extension of the number system. The word decimal means by 10. The numbers which are expressed in the decimal form is known as a decimal. There are two parts in the decimal numbers that include whole numbers and decimal parts. Decimals are represented by the symbol ‘.’

### Types of Decimals

There are two types of decimal numbers. They are

1. Terminating decimal

2. non-terminating decimal

**1. Terminating decimal:**

Terminating decimals are decimals that have a finite number of digits after the decimal point. It is also known as the exact decimal numbers.

**2. Non-terminating Decimal:**

Non-terminating decimals are decimal numbers that have an infinite number of digits after the decimal point. Again they are divided into two types they are Recurring decimal numbers and non-recurring decimal numbers.

### Properties of Division of Decimal Numbers

The main properties of the division of decimal numbers are given below.

- When a decimal number is divided by 1, the quotient of the decimal number will be itself.
- Any decimal number is divided by the same number then the quotient will be 1.
- If 0 is divided by any decimal number, the quotient is 0.
- Any decimal number divided by 0 will be undefined.

### Dividing Decimals Properties Examples

Let us discuss the properties of dividing decimal numbers with examples from below.

**Example 1. **

Find the quotient of 132 Ã· 6?

**Solution:**

To perform the division ignoring decimal point.

Put the decimal point in the quotient in such as way that the decimal places in the quotient become equal to the decimal places in the dividend.

13.132 Ã· 6 = 5.188

Therefore, we see that both dividend and quotient have the same decimal places there is 3.

**Example 2. **

The Product of two decimal numbers is 483.21 if one of them is 28.13 then what is the other number?

**Solution:**

The product of two numbers is 483.21

One number is 28.13

The other number = 483.21 Ã· 28.13

483.21/28.13 Ã· 100/100

48321/2813 = 17.17

The other number is 17.17

**Example 3.**

There are some bags of coffee power each weighing 86.3 kg. If the total weight of all the bags is 346.2 kg. Find the total number of bags?

**Solution:**

Given,

Total weight of all the bags = 345.2 kg

Each bag weight = 86.3 kg

Total number of bags = 345.2/86.3

345.2/86.3 Ã— 10/10

The required number of bags = 4

**Example 4. **

Ruby divide $1387.30 equally among his 42 friends. How much does each friend get?

**Solution:**

Given,

Total money = $ 1287.30

Total number of friends = 42

Each man get = $(1387 Ã· 42)

Therefore each man get $33.03

**Example 5. **

The total cost of 10 pencils is Rs. 384.10 find the cost of 2 pencils?

**Solution:**

Given,

Cost of 10 pencils = Rs. 384.10

Cost of 1 pencil = 384.10/10 = Rs. 38.41

Cost of one pencil is Rs. 38.41

Cost of 2 pencils is 2 Ã— 38.41 = Rs. 76.82

Therefore the cost of 2 pencils is Rs. 76.82

**Example 6.**

i.) 2.3 Ã· 1 = 2.3

Any number divided by 1 is itself.

Hence the given property is proved.

ii.) 5.65 Ã· 1 = 5.65

Any number divided by 1 is itself.

Hence the given property is proved.

**Example 7.**

i.) 5.6 Ã· 5.6 = 1

When we divide 5.6 by 5.6 the remainder will be 0 and the quotient is 1.

Thus the given property is true.

ii.) 1.001 Ã· 1.001 = 1

When we divide 1.001 by 1.001 the remainder will be 0 and the quotient is 1.

Hence the given property is true.

**Example 8.**

i.) 0 Ã· 0.25 = 0

In the given problem we are dividing 0 by 0.25 we will get the quotient as 0.

ii.) 0 Ã· 1.49 = 0

In the given problem we are dividing 0 by 1.49 we will get the quotient as 0.

### FAQs on Properties of Dividing Decimals

**1. What is the division of decimal numbers?**

When we divide decimals we will change the decimal into a whole number by shifting the decimal point to the right. Then move the decimal point of the dividend up to the same number of places to the right and divide the resultant numbers in a regular way.

**2. What are the four rules of decimals?**

The four basic operations involving decimals are addition, subtraction, multiplication, and division.

**3. Is a decimal number divided by itself is 1?**

When the decimal number is divided by itself the quotient is 1.