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.