# Pattern of Rational Numbers

Discussion in 'Algebra' started by nycmathguy, Apr 8, 2022.

1. ### nycmathguy

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College Algebra
Chapter 1
Section 1

nycmathguy, Apr 8, 2022

2. ### MathLover1

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A fraction, reduced to lowest terms, will correspond to a terminating decimal if and only if the prime factorization of the denominator has only powers of 2 and 5. If there are any other factors it will be an infinitely repeating decimal.

So, the condition required for a rational number to have a terminating decimal expansion is that when the number is in its simplest form then its denominator should be in the form of 2^m * 5^n ( where m and n are any whole number ).

MathLover1, Apr 8, 2022
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3. ### nycmathguy

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You lost me there with 2 and 5. Why those two particular numbers?

nycmathguy, Apr 8, 2022
4. ### MathLover1

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2 and 5 are the prime numbers

MathLover1, Apr 8, 2022
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5. ### nycmathguy

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You selected 2 and 5 but could have chosen any other set of prime numbers.

nycmathguy, Apr 8, 2022
6. ### MathLover1

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read again: A fraction, reduced to lowest terms, will correspond to a terminating decimal if and only if the prime factorization of the denominator has only powers of 2 and 5.

MathLover1, Apr 8, 2022
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7. ### nycmathguy

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It pays to read slowly and carefully.

nycmathguy, Apr 8, 2022