A repeating decimal is just a decimal that repeats. An example would be 6.575757... Repeating decimals are infinite.
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An example of a repeating decimal is the fraction 1/6. One sixth equals zero point one six six repeating.
You know a decimal is repeating when you keep getting the same remainder and you keep adding the same decimal onto the end. On calculators it may be expressed as, as an example, 0.6666667. When writing a reoccurring (repeating) decimal it is usually expressed as one decimal with a line over the top of it.
When you convert a fraction to a decimal sometimes the decimal repeats forever. For example 1/3 as a decimal = 0.333333333.... (or 0.3 "recurring"). Another example is 1/7=0.142857142857.... (or 0.142857 recurring).
A and b
Either, the decimal with a line over what's repeating (eg. 0.6 with a line over it), or decimal repeating (eg. "point six repeating").