Question

Question #92413

Answer 1

`0.1bar(23)=61/495`

Explanation:

Let... `x` be the decimal repeating one
`x=0.1bar(2323)` `larr larr larr larr larr larr larr`

Now.... notice that if you'll subtract this `uarr` from `1000x`... it'll be hard and stupid to subtract... so we'll take `10x` so that it'll be easy to subtract
`10x=1.bar(2323)`.....(1)

Now... multiply this equation by `1000` to get the decimals on on side to subtract easily
`1000x=123.bar(23232323`......(2)

Subtract equation 1 from equation 2
`1000x-10x=123.bar(23)-1.bar(23`

That gives
`990x=122`

Transfer `990`
`x=122/990rArrx=61/495`

Now.. as the numerator is a prime number and the denominator is not divisible by the denominator.... it is the answer