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

1 Answer
sente
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#

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