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Look at several examples of rational numbers in the form p/q (q ≠ 0), where p and q are integers with no common factors other than 1 and having terminating decimal representations (expansions).
Rational numbers of the form p/ q , (q ≠ 0) can be 1/4, 7/8, 37/25, 639/250, 7/16, 11/25 , ... etc., which have terminating decimal representations. According to the definition of terminating decimal, when the denominator of rational number is in the power of 2 or 5 or both, then such rational numbers give a terminating decimal. In other words, it can also be said that to represent the rational number p/q . (q ≠ 0) in terminating decimal form, it is necessary that every q be taken as the prime factorization of q only to the power of 2 or power of 5 or both.
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