How do you convert 0.27 (27 being repeated) to a fraction?

1 Answer
Feb 24, 2016

#0.bar(27) = 3/11#

Explanation:

The standard notation for a repeating decimal is to put a bar over the repeating digits, that is, #0.27272727... = 0.bar(27)#

Let #x = 0.bar(27)#

#=> 100x = 27.bar(27)#

#=> 100x - x = 27.bar(27)-0.bar(27)#

#=>99x = 27#

#=> x = 27/99 = 3/11#

This trick works in general for repeating decimals. The idea is to multiply by a power of #10# which will result in the same repeating decimal after multiplication, that is, #10^n# where there are #n# digits in the sequence which repeats.