Question

write whether the rational number 7/75 will have a termination decimal expansion or a nor-terminating repeating decimal expansion.

Answer 1

7/75 will have a non terminating but repeating decimal expantion

Answer 2

Answer:

It is non terminating repeating decimal.

Step-by-step explanation:

Given : Rational number  $\frac{7}{75}$       

To find : Write whether the rational number will have a terminating or a non terminating repeating decimal expansion?

Solution :

Terminating decimal is a fraction which decimal form is up to limited place it can be repeated or non repeat.

Non terminating repeating Decimal whose decimal forms is repeated and doesn't end.

Rational number  

$\frac{7}{75}$

Denominator is 75  

If Denominator satisfy or in the form ${2}^{m}\times{5}^{n}$

I will be Terminating decimal.

So,  

$\frac{7}{75}=\frac{7}{ {3}^{1}\times{5}^{2} }$

The denominator is not satisfying the form.

Therefore, It is non terminating repeating decimal.