Terminating numbers are decimal representations of rational numbers.
Nonterminating numbers may or may not be rational numbers.
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There are are three types of decimals: terminating, repeating and non-terminating/non-repeating. The first two are rational, the third is not.
Rational numbers can be expressed as a terminating or repeating decimal.
they always are.
It is called a rational number. The rational numbers are closed under the operations of addition, subtraction, multiplication, and division (not dividing by 0). The fact that it is not terminating is not important at all. In fact, if we use other bases besides base 10, we will see that the set of numbers that are rational or irrational doesn't change. However, if we use another base, for example base 3, then the number 1/3 in base 3 can be represented with a terminating "decimal" (technically not decimal). The set of rational numbers that have terminating "decimals" depends on the base.