How do you solve non-terminating repeating decimal?

Answer 1

Presumably you want to convert that into a fraction. Here is an example.

Your number is 0.4121212... ("12" is repeated)

Call this "x":

x = 0.4121212...

Multiply this by 100 (if three digits repeat, multiply by 1000, if 4 digits repeat, by 10,000, etc.), and subtract:

100x = 12.21212...

x = 0.41212...

99x = 11.8

Therefore, x = 11.8 / 99 = 118/990.

The final step is to see whether you can simplify the fraction.