# Division of Decimal Fractions

The rules of division of decimal fractions by 10, 100, 1000 etc. are discussed here.

(i) While dividing a decimal by 10, 100, or 1000 etc. i.e., multiples of 10, the decimal shifts to the left by as many places as there are zeroes in the divisor.

(ii) If the number of places in the integral part is less, then put the required number of zeroes to the left of the integral part, then shift the decimal point.

1. 71.6 ÷ 10

Solution:

71.6 ÷ 10

716/10 ÷ 10

= 716/10 × 1/10

= 716/100

= 71.6 ÷10

= 7.16

Therefore, 71.6 ÷ 10 = 7.16

Here we observe that decimal moves one place to the left.

2. 923.07 ÷ 100

Solution:

923.07 ÷ 100

= 92307/100 ÷ 100

= 92307/100 × 1/100

= 92307/10000

= 9.2307

Therefore, 923.07 ÷ 100 = 9.2307

Here we observe that decimal shifts two places to the left.

3. 44.008 ÷ 1000

Solution:

44.008 ÷ 1000

44.008/1000 ÷ 1000

= 44008/1000 × 1/1000

= 44008/1000000

=0.044008

Therefore, 44.008 ÷ 1000 = 0.044008

Here we observe that decimal point shifts three places to the left.

Let us consider some of the examples of division of decimal fractions by 10, 100, 1000, etc….

(i) 17.1 ÷ 10

Here the decimal shifts to the left by as many places as there are zeroes in the divisor.

Since there is 1 zero in the divisor then the decimal shifts 1 place to the left.

Therefore, 17.1 ÷ 10 = 1.71

(ii) 42.08 ÷ 10

Since there is 1 zero in the divisor then the decimal shifts 1 place to the left.

Therefore, 42.08 ÷ 10 = 4.208

(iii) 2.1 ÷ 100

We observe that the number of places in the integral part is less, then put the required number of zeroes to the left of the integral part, then shift the decimal point.

Since there are 2 zeroes in the divisor then the decimal shifts 2 places to the left.

Therefore, 2.1 ÷ 100 = 0.021

(iv) 73.3 ÷ 100

We observe that the number of places in the integral part is less, then put the required number of zeroes to the left of the integral part, then shift the decimal point.

Since there are 2 zeroes in the divisor then the decimal shifts 2 places to the left.

Therefore, 73.3 ÷ 100 = 0.733

(v) 81.6 ÷ 1000

We observe that the number of places in the integral part is less, then put the required number of zeroes to the left of the integral part, then shift the decimal point.

Since there are 3 zeroes in the divisor then the decimal shifts 3 places to the left.

Therefore, 81.6 ÷ 1000 = 0.0816

(vi) 984.72 ÷ 1000

We observe that the number of places in the integral part is less, then put the required number of zeroes to the left of the integral part, then shift the decimal point.

Since there are 3 zeroes in the divisor then the decimal shifts 3 places to the left.

Therefore, 984.72 ÷ 1000 = 0.98472

Choose the right answer and fill in the blank.

(i) 478.65 ÷ ________ = 47.865

(a) 10

(b) 100

(c) 1000

(d) 1

(ii) 137.85 × 10 = ________

(a) 13785

(b) 13.785

(c) 1378.5

(d) 1.3785