Question

if u have a 2 digit reapeating decimal how do u convert it into a fraction ex.) 0.023 but 23 ia reapeting over and over how do u convert it to a fraction

Answer 1

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.