Question

What is .94 repeating with both numbers repeating?

Answer 1

`0.bar(94) = 94/99`

Explanation:

Note that we can write `0.94949494...` with a viniculum (over bar) to indicate the group of repeating digits, as `0.bar(94)`

One method is to find an integer multiple of `0.bar(94)` that results in an integer, then divide by it, like so...

`(100-1) 0.bar(94) = 94.bar(94) - 0.bar(94) = 94`

So:

`0.bar(94) = 94/(100-1) = 94/99`

Note that `94` and `99` have no common factor larger than `1`, so this is in simplest form.

Alternatively, you can start by recognising that:

`1 = 0.999999.... = 0.bar(99)`

Then:

`0.949494... = (0.bar(94))/(0.bar(99)) = 94/99`