Question

Which of the following is a non-terminating repeating decimal?
(A) $\dfrac{35}{14}$
(B) $\dfrac{14}{35}$
(C) $\dfrac{1}{7}$
(D) $\dfrac{7}{8}$

Answer 1

Hint: At first convert the fraction into decimal and then analyze each and give the answer.
In the question, we are asked to find which of the given fractions can be represented as non-terminating repeating decimals.

Complete step-by-step answer:

First let’s define what non-terminating repeating decimals are.

A non-terminating repeating decimal is a decimal fraction that never comes to an end but repeats one or more numbers after the decimal point in a predictable pattern.

Just like $\dfrac{22}{7}$ which is equal to 3.142857148285714….. . In this we can see that after decimal at an interval of 6 places means after decimal 142857 digits are repeating again and again.

Also, like for an example $\dfrac{10}{3}$ which is equal to 3.3333…. in this we can see that after decimal digit 3 is repeating again and again.

This 2 above are the examples of non terminating decimal fraction.

This type of decimal is also converted to rational numbers of the form $\dfrac{p}{q}$ where $q\ne 0$.

Now we will analyze each of the following options given.

a) $\dfrac{35}{14}$ , this fraction can be reduced into simpler terms and we get $\dfrac{5}{2}$ which is evaluated as 2.5 which is terminating. Hence, (A) option is incorrect.

b) $\dfrac{14}{35}$, this fraction can be reduced into simpler terms and we get $\dfrac{2}{5}$ which is evaluated as 0.4 which is terminating. Hence, (B) option is incorrect.

c) $\dfrac{1}{7}$, this fraction converting into decimal, we get 0.14285714285714…. we see that after decimal at an interval of 6 places digits are repeating and non terminating. Hence, (C) option is correct.

(d) $\dfrac{7}{8}$, this fraction on simplification and converting to decimal we get, 0.875 which is terminating. Hence, (D) is incorrect.

The correct option is ‘C’.

Note: One can also check by first factoring the denominator after reducing the fraction into simpler terms. If factors only contain either 2 or 5 or both then they are non-terminating. So, we have to eliminate those.