Question

What is 0.15 repeating as a fraction?

Answer 1

See a solution process below;

Explanation:

I am assuming the `1` and the `5` repeat as `0.151515...`

If it is just the `5` repeating you can use this same process.

First, we can write:

`x = 0.bar15`

Next, we can multiply each side by `100` giving:

`100x = 15.bar15`

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

`100x - x = 15.bar15 - 0.bar15`

We can now solve for `x` as follows:

`100x - 1x = (15 + 0.bar15) - 0.bar15`

`(100 - 1)x = 15 + 0.bar15 - 0.bar15`

`99x = 15 + (0.bar15 - 0.bar15)`

`99x = 15 + 0`

`99x = 15`

`(99x)/color(red)(99) = 15/color(red)(99)`

`(color(red)(cancel(color(black)(99)))x)/cancel(color(red)(99)) = (3 xx 5)/color(red)(3 xx 33)`

`x = (color(red)(cancel(color(black)(3))) xx 5)/color(red)(color(black)(cancel(color(red)(3))) xx 33)`

`x = 5/33`