Express \(15.\bar { 712 }\) as a fraction in the simplest form.

1.	Express \(15.\bar { 712 }\) as a fraction in the simplest form.
Answer» Let x = \(15.\bar { 712 }\) i.e. x = 15.7121212 …(1) Multiplying (1) by 10 and 100 successively, we get 10x = 157.121212 …(2) and 1000x = 15712.1212 …(3) Subtracting (2) from (3), we get 1000x – 10x = (15712.1212…) – (157.1212…) ⇒ 990x = 15555 ⇒ x = \(\frac { 15555 }{ 990 }\) ⇒ x = \(\frac { 1037 }{ 66 }\) Hence, \(15.\bar { 712 }\) = \(\frac { 1037 }{ 66 }\)

Answer»

Let x = \(15.\bar { 712 }\)

i.e. x = 15.7121212 …(1)

Multiplying (1) by 10 and 100 successively, we get

10x = 157.121212 …(2)

and 1000x = 15712.1212 …(3)

Subtracting (2) from (3), we get

1000x – 10x = (15712.1212…) – (157.1212…)

⇒ 990x = 15555

⇒ x = \(\frac { 15555 }{ 990 }\)

⇒ x = \(\frac { 1037 }{ 66 }\)

Hence, \(15.\bar { 712 }\) = \(\frac { 1037 }{ 66 }\)

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