Almost 60 years after taking my last math class, I discovered how to turn a repeating decimal into its equivalent fraction.
-- Take the set of digits that repeats, no matter how many digits there are. Write them as the numerator of a fraction.
-- For the denominator, write the same number of '9's.
-- If it's possible and you feel like it, simplify (reduce) the fraction.
You have 0.023 with the 23 (two digits) repeating forever.
-- Write the 23 (two digits) as the numerator.
-- Write 99 (two digits) as the denominator.
Now you have the fraction 23 / 99 . It can't be reduced.
You actually had 0.0... before the repeating part. That just means that the fraction has been divided by 10. The real equivalent fraction is 23 / 990 . (Which also can't be reduced.)
After so many years not knowing how to do it, this still blows my mind. Just now, I punched " 23/990 "into my calculator, and stared in wonder and amazement when " 0.023232323 " came up.
