(i) 0.666…

(ii) 0.4777…

(iii) 0.001001001…

NCERT Class 9 Math’s Chapter 1

Page No. 14

Exercise 1.3

Question No. 3

# Express the following in the form p/q , where p and q are integers and q ≠ 0.

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(i) 0.666…

Let x = 0.666…

⇒ x = 0.6666… …(i)

Multiplying equation (i) by 10 both sides

10x = 6.6666..

⇒ 10x = 6 + 0.6666…

⇒ 10x = 6 + x [From equation (i)]

⇒ 10x x = 6

⇒ 9x = 6

⇒ x = 6/9 = 2/3

(ii) 0.4777…

Let x = 0.4777…

⇒ x = 0.47777… …(i)

Multiplying equation (i) by 10 both sides

⇒ 10x = 4.7777… …(ii)

Multiplying equation (ii) by 10 both sides

⇒ 100x = 47.7777…

⇒ 100x = 43 + 4.7777…

⇒ 100x = 43 + 10x [From equation (ii)]

⇒ 100x = 10x = 43

⇒ 90x = 43

⇒ x = 43/90

(iii) 0.001001001…

Let x = 0.001001001…

⇒ x = 0.001001001…

Multiplying equation (i) by 1000 both sides

1000x = 1.001001001…

⇒ 1000x = 1 + 0.001001001…

⇒ 1000x = 1 = x [From equation (i)]

⇒ 1000x – x = 1

⇒ 999x = 1

⇒ x = 1/999

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