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Find the value of 0.3258....

Find the value of `0.3258.`

Text Solution

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Let `R = 0.32 bar(58) rArr R = 0.32585858`.... ...(i)
Here number of figure which are not recurring is 2 and number of figure which are recurring is also 2.
then `100 R = 32.585858..` ....(ii)
and `10000 R = 3258.5858...` ....(iii)
Substracting (ii) from (iii), we get
`9900 R = 3226 rArr R = (1613)/(4950)`
Aliter Method : `R = .32 + .0058 + .0058 + .000058 +` .....
`= .32 + (58)/(10^(4)) (1 + (1)/(10^(2)) + (1)/(10^(4)) + ....oo)`
`= .32 + (58)/(10^(4)) ((1)/(1 - (1)/(100)))`
`= (32)/(100) + (58)/(9900) = (3168 + 58)/(9900) = (3226)/(9900) = (1613)/(4950)`
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