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Express 0.2overline25 as a rational num...

Express `0.2overline25` as a rational number.

Text Solution

Verified by Experts

In `0.overline225` , periodicity `=2`.
So, multiply the decimal fraction by 100 an subtract the original number form the proudct.
let `0.overline225 =x` . Then , `x=0.2252525......` and `100x=22.525252......` Subtracing x from `100x`, we get
`100x =22.5252...`
`(-)x=2252.....`
`99x=22.3`
`x=(22.3)/(99)=(223)/(990)`.
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