How you would convert the repeating, nonterminating decimal to a fraction? Explain the process as you solve the problem. 0.1515 . . .

Answer 1

converting n, a repeating decimal...
100n-n=15.000000
but 100n-n=99n

so then think this out
.1515=15/99

Answer 2

let x = .151515
the length of the repeating period is 2 digits, so multiply by 10^2 or 100
100x = 15.151515...
x = .151515..
subtract them:
99x = 15
x = 15/99

If you have decimal which contains a repeating sequence after some decimals that don't repeat ...
e.g. 0.12456456456..
let x= .12456456456..
the length of the repeat is 3, so multiply by 1000
1000x = 124.56456456..
x = .12456456456
subtract:
999x =124.440000..
x = 124.44/999
=12444/99900
= 1037/8325