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Find the rational number whose decimal e...

Find the rational number whose decimal expansion is given below :
(i) `0.bar(3)` (ii) `0.bar(231)` (iii) `3.bar(52)`

Text Solution

Verified by Experts

The correct Answer is:
(i) `1/3` (ii) `231/999` (iii) `317/90`
(ii) `x=0.231231231...` and `1000x=231.231231231...`
On subraction, we get `999x=231 rArr x=231/999`.
Hence, `bar(0.231)=231/999`.
(iii) `x=3.5222... rArr 10x=35.222...` and `100x=352.222`...
`:. 90x=317 rArr x=317/90`.
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