Terminating and Repeating Decimals
Any rational number (that is, a fraction in lowest terms) can be written as either a terminating decimal or a repeating decimal. Just divide the numerator by the denominator. If you end up with a remainder of 0, then you have a terminating decimal. Otherwise, the remainders will begin to repeat after some point, and you have a repeating decimal.
Example:
Convert the fraction 5/8 to a decimal.
The division is as follows:
So, 5/8 = 0.625. This is a terminating decimal.
Example:
Convert the fraction 7/12 to a decimal.
The division is as follows:
So:
This is a repeating decimal.
See also Converting Repeating Decimals to Fractions.
