Question

Has the rational number a terminating or a non terminating decimal 441 / 2² X 5⁷ X 7²
representation?

Answer 1

441/ 2^2 * 5^7 * 7^2 has  non-terminating decimal expansion.

Step-by-step explanation:

We have 441/ 2^2 * 5^7 * 7^2.

Let the number be expressed as a/b, a rational number, such that the prime factors of q are not of the form  2^n * 5^m where m and n are non-negative integers.

Then, a/b 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^n * 5^m.

So it is non-terminating decimal expansion.