Question

A rational number in its decimal expansion is 1.7112 what can you say about the prime factor of q. When this number is expressed in the form of p/q ?

Answer 1

Hi ,

Let x = 1.7112

x = 17112/ 10000 = p/q

q = 10000

q = ( 10 )⁴

q = ( 2 × 5 )⁴

q = 2⁴ × 5⁴ = 2^n × 5^m

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Let x = p/q be a rational number, 

such that the prime factorization of

q is of the form 2^n × 5^m , where 

n and m are non - negative integers.

Then x has a decimal expansion 

which terminates.

I hope this helps you.