Here in this topic we will discuss about the different properties of division of a decimal number. These properties of division of decimal numbers are important for the learners as it will enrich their knowledge and will help them in better understanding of the sums. We have previously learnt the properties of multiplication of decimal numbers and here we will study the properties of division in case of decimal numbers.

The properties of division of decimal numbers are illustrated below:

**Property I:**

When a decimal number is divided by 1 the result is the decimal number itself

Here are few examples to illustrate property 1

(i)195.02 ÷ 1 =195.02

(ii) 155.35 ÷ 1 = 155.35

(iii) 86.26 ÷ 1 = 86.25

(iv) 59.25 ÷ 1 = 59.25

(v) 70.25 ÷ 1 =70.25

(vi) 175.25 ÷ 1 = 175.25

(vii) 75.25 ÷ 1 = 75.25

(viii) 41.10 ÷ 1 = 41.10

(ix) 93.52 ÷ 1 = 93.52

(x) 142.23 ÷ 1 = 142.23

In all these examples we can see that that when a decimal fraction is divided by 1 the quotient is the decimal fraction itself

**Property II:**

When a decimal number is divided by the same decimal number then the result is 1

Here are few examples to illustrate property 2

(i) 75.25 ÷ 75.25 = 1

(ii) 155.35 ÷ 155.35 = 1

(iii) 86.26 ÷ 86.26 = 1

(iv) 142.23 ÷ 142.23 = 1

(v) 59.25 ÷ 59.25 = 1

(vi) 175.25 ÷ 175.25 = 1

(vii) 195.02 ÷ 195.02 =1

(viii) 41.10 ÷ 41.10 = 1

(ix) 93.52 ÷ 93.52 = 1

(x) 70.25 ÷ 70.25 =1

In all these examples we can see that that when a decimal fraction is divided by itself the quotient is 1

**Property III:**

When zero is divided by any decimal number the result is zero.

Here are few examples to illustrate property 3

(i) 0 ÷ 175.25 = 0

(ii) 0 ÷ 195.02 =0

(iii) 0 ÷ 41.10 = 0

(iv) 0 ÷ 75.25 = 0

(v) 0 ÷ 155.35 = 0

(vi) 0 ÷ 86.26 = 0

(vii) 0 ÷ 142.23 = 0

(viii) 0 ÷ 5.35 = 0

(ix) 0 ÷ 88.001 = 0

(x) 0 ÷ 42.32 = 0

In all these examples we can see that that when zero is divided by any decimal fraction the quotient is 0

**Property IV:**

We cannot divide any decimal number by zero as the reciprocal of zero does not exists hence it cannot be divided.

**Here are few more examples for practice based on the properties of division of decimal:**

1. 58.63 ÷ 58.63= …………………

2. 89.23 ÷ 1= …………………

3. 0 ÷ 7.54= …………………

4. 85.20 ÷ ………………… = 1

5. ………………… ÷ 0.2103 = 0

6. 30.25 ÷ ………………… = 30.25

7. 55.01 ÷ 55.01 = …………………

8. ………………… ÷ 0.541 = 0

9. 7.004 ÷ 1 = …………………

10. 314.51 ÷ 314.51 = …………………

**Answers:**

1. 1

2. 89.23

3. 0

4. 85.20

5. 0

6. 1

7. 1

8. 0

9. 7.004

10. 1

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