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

1 Answer
Mar 6, 2016

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.