1.

Express the following in the form p/q, where p and q are  integers and q ≠ 0.(i) \(0.\bar { 6 }\)(ii) \(0.4\bar { 7 }\)(iii) \(0.\bar { 001 }\)

Answer»

(i) \(0.\bar { 6 }\)

Let x = \(0.\bar { 6 }\) (Pure recurring decimal)

i.e. x = 0.6666 …(1)

Multiplying (1) by 10, because ones digit i.e. 6 is repeating, we get

10x = 6.6666 …(2)

Subtracting (1) from (2), we get

10x – x = (6.6666…) – (0.6666…)

⇒ 9x = 6

⇒ x = \(\frac { 6 }{ 9 }\)

⇒ x = \(\frac { 2 }{ 3 }\)

(ii) Let x = \(0.4\bar { 7 }\) (Mixed recurring decimal)

i.e. x = 0.47777 …(1)

Multiplying (1) by 10, to make it pure recurring decimal, we get

10x = 4.7777 …(2)

Further multiplying (2) by 10, we get

100x = 47.777 ….(3)

Subtracting (2) from (3), we get

100x – 10x = (47.777…) – (4.7777…)

⇒ 90x = 43

⇒ x = \(\frac { 43 }{ 90 }\)

(iii) Let x = \(0.\bar { 001 }\)

i.e. x = 0.001001001 …(1)

Multiplying (1) by 1000, we get

1000x = 1.001001 …(2)

Subtracting (1) from (2), we get

1000x – x = (1.001001…) – (0.001001…)

⇒ 999x = 1

⇒ x = \(\frac { 1 }{ 999 }\)


Discussion

No Comment Found

Related InterviewSolutions