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Express 0.2overline(54) as a fractions ...

Express `0.2overline(54)` as a fractions in simplest form.

A

14/65

B

14/75

C

14/55

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
Let x = `0.2overline(54)` then,
x = 0.2545454.
10x= 2.545454
and 1000x = 254.545454…
on subtracting (ii) from (iii) we get
` 990x = 252 Rightarrow x= 252/990 = 126/495 = 42/165 = 14/65`
` 0.2overline(54) = 14/55` \
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