Question

Which of the following has a value of non-terminating decimal.
$
  {\text{A}}{\text{. }}\dfrac{7}{4} \\
  {\text{B}}{\text{. }}\dfrac{6}{5} \\
  {\text{C}}{\text{. }}\dfrac{5}{3} \\
  {\text{D}}{\text{. None of these}} \\
$

Answer 1

Hint: To find the term with non-terminating decimal, we divide each of the following with their respective denominators and see which numbers are absolutely divisible w.r.t their divisors and which are not.

Step-by-step answer:
Given,
Non-terminating decimal, i.e. the decimal value is never ending.
$\dfrac{7}{4}$= 1.75
$\dfrac{6}{5}$= 1.2
$\dfrac{5}{3}$= 1.66666…..
5 is not exactly divisible by 3, every time 3 divides 5 it leaves a remainder 2 and it keeps on going.
Hence $\dfrac{5}{3}$has a non-terminating decimal.
Option C is the correct answer.

Note:In order to solve this type of problems the key is to understand the definition of a non-terminating decimal.
A non-terminating, non-repeating decimal is a decimal number that continues endlessly, with no group of digits repeating endlessly. Decimals of this type cannot be represented as fractions, and as a result are irrational numbers. E.g. π.