How do you convert 0.7 (7 being repeated) to a fraction?

1 Answer
Mar 4, 2016

#0.bar(7) = 7/9#

Explanation:

With the notation of using a bar to denote a repeating digit,

let #x = 0.bar(7)#

#=> 10x = 7.bar(7)#

#=>10x - x = 7.bar(7)-0.bar(7)#

#=>9x = 7#

#=>x = 7/9#

This technique works in general to find the fractional representation of a repeating decimal. Just multiply by #10^n# where #n# is the number of digits that are repeating, then subtract away the original repeating digit and solve for #x#.