1. Let n be the decimal form of a rational number a/b, where a and b are nonzero integers.

a. If n is a terminating decimal, what can be said about the factors of b? Explain.

b. If n is a repeating decimal, what can be said about the number of digits in the repeating block? Explain.

Question

Mathematics

Ruby Edwards

12 April, 20:54

1. Let n be the decimal form of a rational number a/b, where a and b are nonzero integers.

a. If n is a terminating decimal, what can be said about the factors of b? Explain.

b. If n is a repeating decimal, what can be said about the number of digits in the repeating block? Explain.

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Answers (1)

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Kaila Orr · Answer 1

A. Essentially, b is (or can be expressed in an equivalent fraction as) a power of ten. Say the decimal is 0.342, then the fraction would be 342/1000. Ten has two prime factors, 2 and 5. Some factors in increased powers of ten might be canceled out by the numerator, but factors will never be added. Thus, b must have prime factors of only 2 and 5 to terminate.

B. If n is a repeating decimal, the number of digits in the repeating block cannot be more than (b-1). For example, (1/7) has 6 digits in the repeating block.

1. Let n be the decimal form of a rational number a/b, where a and b are nonzero integers.a. If n is a terminating decimal, what can be said about the factors of b? Explain.b. If n is a repeating decimal, what can be said about the number of digits in the repeating block? Explain.

1. Let n be the decimal form of a rational number a/b, where a and b are nonzero integers.

a. If n is a terminating decimal, what can be said about the factors of b? Explain.

b. If n is a repeating decimal, what can be said about the number of digits in the repeating block? Explain.