Question

It's urgent answer this anyone please ​

Answer 1

Answer:

I think 3 is write answer non repeating decimal ✍

Answer 2

Required Answer:-

What's given?

$\Large{ \rm{ \frac{175}{ {2}^{3}. {5}^{3}. {7}^{3} } }}$

The above fraction is not in the simplest form. Hence, the first thing to do is to simplify it.

$\Large{ \rm{ \frac{ \cancel{175}}{ \cancel{ {2}^{3} . {5}^{3} . {7}^{3} }} = \Large{ \frac{1}{ {2}^{3} .5. {7}^{2} } }}}$

How to decide without actual division?

As the above fraction can be represented in the form of p/q, it is a rational number. The decimal expansion of a rational number is either:

• Terminating
• A non-terminating recurring

When the denominator is in the form of ${2}^{m} \times {5}^{n}$, the decimal expansion is terminating. And if not then it is non-terminating recurring.

Hence:-

The denominator of the fraction given in the question is not in the form of ${2}^{m} \times {5}^{n}$ because 7 is also a prime factor of the denominator. Therefore, it is a non-terminating recurring/repeating decimal Option (3).