Question

How do you convert 0.56 (6 being repeated) to a fraction?

Answer 1

`0.5bar(6) = 17/30`

Explanation:

Using the notation of placing a bar over a digit or set of digits to indicate they repeat:

Let `x = 0.5bar(6)`

`=>10x = 5.6bar(6)`

`=>10x-x = 5.bar(6)-0.5bar(6) = 5.1`

`=>9x = 51/10`

`=> x = (51/10)/9=51/90=17/30`

This trick works in general for any number with repeating digits. Multiplying by `10^n` where `n` is the number of digits repeating, and then subtracting the original value eliminates the infinitely repeating portion, allowing us to solve for its fractional form.