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Converting Decimals into Fractions

Using the last decimal place you can determine the proper denominator for the fraction.

Non-repeating finite decimals:

  • Example: Convert 0.76 into a fraction.

0.76 → 6 is in hundreds place; therefore, hundred is proper denominator

\frac{76}{100}\ \rightarrow\ \frac{19}{25}

Repeating decimals:

  • Example: Convert 0.595959\overline{59} into a fraction.

Use a variable to solve.

let x=0.595959\overline{59}

Multiply variable, x, by a power of 10 to get decimal places to line up.

see the last place it repeats: 0.\overline{59} → hundredths place, so multiply x by 100

100x=59.59\overline{59}

100x-x=59.\overline{59}-0.\overline{59}

99x=59

x=\frac{59}{99}