Real Numbers

Mathematics — Second Preparatory

Repeating decimals

A repeating decimal is a decimal that does not end, in which one digit or a group of digits repeats in a regular pattern, such as 0.333… and 0.1212… It is written with a bar over the repeating digits.
Every repeating decimal is a rational number.
To change it into a fraction, follow these steps:

Let x equal the number.
Multiply x by 10, 100 or 1000, depending on how many digits repeat, so that the repeating parts line up after the decimal point.
Subtract the two equations, so the repeating parts cancel.
Solve for x and simplify the fraction.

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