How do you convert non-terminating decimals into fractions?

Answer 1

Here is an example: convert 3.121212... to a fraction.

Solution: Call this number "x". Then:

100x = 312.121212...

x = 3.121212...

Subtract the second equation from the first:

99x = 209

Divide both sides by 99:

x = 209/99

Now all that needs to be done is to simplify the resulting fraction. Such numbers are said to be "irrational".

Note 1: If the digits repeat with a period length of 1, multiply by 10; if the period length is 2 (as in this example), multiply by 100, if the period length is 3, multiply by 1000, etc.

Note 2: If the decimals don't repeat, you can't convert exactly into a fraction.