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Show that 0. 2353535. . .=0. 2 bar 35can...

Show that `0. 2353535. . .=0. 2 bar 35`can be expressed in the form `p/q`, where p and q are integers and `q!=0`.

Text Solution

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`x = 0.bar235`
multiply by `10`
`10x = 2 .bar35`.........eqn(i)
multiply` b 100`
` 1000 x = 235 .bar 35`.......... eqn(ii)
subtracting eqn (ii)- (i)
`990 x = 233`
`x=233/990`
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