as a rational number.
This is very similar to the previous problem. We use the repeating pattern to break up the decimal into a sum of fractions:
Since the repeating pattern is 2 digits long, we have to multiply each fraction by to get to the next fraction. We have a geometric series with and .
The sum of this series is
If we put the fraction into a calculator, we get something very close to 0.787878.... This is a good sanity check.