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A terminating decimal is something like .25, where a repeating decimal is something like 1/3
A terminating number has a definitive value - A repeating number continues indefinitely. For example - 10 divided by 8 is 0.125 (a terminating number) - 10 divided by 3 is 3.333333 (the decimal repeats indefinitely).
A terminating decimal is a decimal that ends. A repeating decimal is a decimal that goes on and on.
They are both representations of rational numbers.
If a number consists of a series of non repeating and non terminating digits then it is irrational.A particularly well known example is that of pi (which is an irrational number representing the proportion between the diameter of a circle and its circumference).