Question

Has the rational number \[\frac{441}{2^2 \times 5^7 \times 7^2}\] a terminating or a nonterminating decimal representation?

Answer 1

We have, 

`441/(2^2xx5^7xx7^2)`

Theorem states: 

Let  `x=p/q` be a rational number, such that the prime factorization of q is not of the form  `2^nxx5^m` , where mand n are non-negative integers.

Then, x has a decimal expression which is non-terminating repeating.

This is clear that the prime factorization of the denominator is not of the form `2^nxx5^m` .

Hence, it has non-terminating decimal representation.