Pattern of Rational Numbers

[nycmathguy]

College Algebra
Chapter 1
Section 1

 

[MathLover1]

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 ).

 

[nycmathguy]

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?

 

[MathLover1]

2 and 5 are the prime numbers

 

[nycmathguy]

2 and 5 are the prime numbers

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

 

[MathLover1]

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.

 

[nycmathguy]

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.

It pays to read slowly and carefully.