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Express 0.overline57 in the form (p)/(q)...

Express `0.overline57` in the form `(p)/(q)` , where p and q are integers and `q ne 0` .

A

`(19)/(31)`.

B

`(18)/(31)`.

C

`(19)/(33)`.

D

`(29)/(31)`.

Text Solution

Verified by Experts

The correct Answer is:
C
Let `x = 0.overline57`
Then, `x = 0.575757….`
Since the repeating block 57 has two digits, we multiply x by 100 to get
`100 x = 57.5757…..`
Subtracting (i) from (ii), we get
`99x = 57 hArr x = (57)/(99) = (19)/(33)`
Hence, `0.overline57= (19)/(33)`.
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