How do you convert 0.1624 (24 being repeated) to a fraction?

1 Answer
Mar 10, 2016

#0.16bar(24) = 134/825#

Explanation:

Multiply by #10000-100# to get an integer:

#(10000-100)*0.16bar(24) = 1624.bar(24) - 16.bar(24) = 1608#

Then divide both sides by #(10000-100)# as follows:

#0.16bar(24) = 1608/(10000-100) = 1608/9900 = (color(red)(cancel(color(black)(12)))*134)/(color(red)(cancel(color(black)(12)))*825) = 134/825#