Question

Find an equivalent fraction for the repeating decimal 12.713?

Answer 1

See a solution process below:

Explanation:

First, we can write:

`x = 12.bar713`

Next, we can multiply each side by `1000` giving:

`1000x = 12713.bar713`

Then we can subtract each side of the first equation from each side of the second equation giving:

`1000x - x = 12713.bar713 - 12.bar713`

We can now solve for `x` as follows:

`1000x - 1x = (12713 + 0.bar713) - (12 + 0.bar713`

`(1000 - 1)x = 12713 - 12 + 0.bar713 - 0.bar713`

`999x = 12701 + (0.bar15 - 0.bar15)`

`999x = 12701 + 0`

`999x = 12701`

`(999x)/color(red)(999) = 12701/color(red)(999)`

`(color(red)(cancel(color(black)(999)))x)/cancel(color(red)(999)) = 12701/999`

`x = 12701/999`