What are repeating and non repeating decimals?

Answer 1

A repeating decimal is a decimal that, well, repeats itself! Like .33333333333333....... The threes never end, they just keep going. Non-reapeting are decimals like .5 or .3 or .57. They end! :)

Answer 2

A repeating decimal is one in which, after a finite number of digits after the decimal place, there is a string of a finite number of digits that repeats again and again and again ... forever. With non-repeating decimals this never happens.

The reasons for using the complicated looking "finite number" phrase twice in the description of repeating decimals is to avoid the trap that many will fall into in answering such a question.

The first is that the repetition need not start straight after the decimal point. For example, 13/36 = 0.036111... with the 1s going on forever. The repetition does not start until the fourth digit after the decimal point. If you replace 36 by 360 it will not start until the fifth digit. And so on.

The second reason is that the repeating string can be of any finite length. For example, 13/42 = 0.3095238095238... (the repeating string is 095238). Obviously, a repeating string cannot be of infinite length because if it were, the first occurrence would never end and so a repeat could never start.