Question

a rational number is in its decimal expansion 1.7112 what can you say about the prime factor of q when number is in the form of p/q​

Answer 1

Answer:

Step-by-step explanation:  

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

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 UwU