Question

Does 441/2^2x5^7x7^2 have terminating or non terminating decimal representation? Answer has been given as non terminating but if it's actually divided it terminates . So what's the actual answer?

Answer 1

A number is terminating if the denominator is of the form
${2}^{m} \times {5}^{n}$
If and only if the number cannot be further simplified.
Now for the question,
$\frac{441}{ {2}^{2} \times {5}^{7} \times {7}^{2} } = \frac{9}{ {2}^{2} \times {5}^{7} }$
Now this cannot be divided further . And the denominator is of the form
${2}^{m} \times {5}^{n}$
Thus the given number is terminating and the answer given is wrong!!