Question

Can anyone explain how to figure out if a fraction or decimal is terminating or repeating decimal?

Answer 1

Answer: A repeating decimal repeats a pattern of the same number. Like 6.7878, that goes on for infinity. When there is a repeating decimal, a line is placed on top of the pattern. A terminating decimal is the opposite and doesn't repeat.

Answer 2

To find out whether a fraction will have a terminating or recurring decimal, look at the prime factors of the denominator when the fraction is in its most simple form. If they are made up of 2s and/or 5s, the decimal will terminate. If the prime factors of the denominator contain any other numbers, the decimal will recur.

Some decimals are irrational, which means that the decimals go on forever but not in a pattern (they are not recurring). An example of this would be pi or
`\sqrt{ 2`.

Explanation: