Pattern of Rational Numbers

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College Algebra
Chapter 1
Section 1

Screenshot_20220407-202452_Samsung Notes.jpg
 
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 ).
 
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 ).

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

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