How do you convert 32.32 (32 being repeated) to a fraction?

1 Answer
Feb 21, 2016

Set up an algebraic equation and solve to find that

32.bar(32)=3200/99

Explanation:

Let x = 0.bar(32)

=>100x = 32.bar(32)

=>100x - x = 32.bar(32) - 0.bar(32)

=>99x = 32

=> x = 32/99

Noting that 100x was equal to the desired value, we may proceed from there (note that if this wasn't the case, for example, if the integer part was different, we could still simply add the integer to get a result).

32.bar(32) = 100x

=100*32/99

=3200/99