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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 , then you have a terminating decimal. Otherwise, the remainders will begin to repeat after some point, and you have a repeating decimal.
Example 1:
Convert the fraction to a decimal.
The division is as follows:
So, . This is a terminating decimal.
Example 2:
Convert the fraction to a decimal.
The division is as follows:
So:
This is a repeating decimal.
The bar over the number, in this case , indicates the number or block of numbers that repeat unendingly.
See also Converting Repeating Decimals to Fractions .