Question

The non terminating non – recurring decimal number cannot be represented as
A. irrational number
B. rational number
C. real number
D. none of these

Answer 1

Hint: A non terminating non-recurring decimal number continues endlessly and no number or pattern repeated.
We always approximate its value upto two decimal places or three places.

Complete step-by-step answer:
In general non terminating means which we cannot terminate and non-recurring means which doesn’t repeat any pattern. So we can say a non terminating and non repeating decimal number continues endlessly and there is no repeating number or pattern in it.
For example $\pi ,e$ is non terminating non recurring decimal number.
So we can say non terminating non recurring decimal numbers are irrational numbers because we cannot convert it into fractions.
So, The non terminating non – recurring decimal number cannot be represented as a rational number.
Hence option B is correct.

Note: We need to read statements very carefully because non terminating and recurring decimal expansion is a rational number.