Question

Decimal expansion of a rational number cannot be
A. non-terminating and non-recurring
B. non-terminating and recurring
C. terminating
D. none of these

Answer 1

Hint: We first find the relation between rational and irrational numbers with their characteristics. For terminating and non-terminating decimal numbers, we find their parts and their relation with rational and irrational numbers. We explain with use of examples.

Complete step-by-step answer:
We find the relation between rational and irrational numbers with their characteristics of being terminating and recurring.
We know that all terminating decimal numbers are rational.
For example, we have $ 0.635=\dfrac{127}{200} $ .
Recurring and non-recurring decimal numbers are parts of non-terminating decimal numbers.
If the decimal is recurring then it is a rational number and if it is non-recurring then it is an irrational number.
For example, we have $ 0.6\overline{35}=\dfrac{635-6}{990}=\dfrac{629}{990} $ and \[\sqrt{11}\text{=3}\text{.31662479}...\].
From the above explained conditions we can say that decimal expansion of a rational number cannot be non-terminating and non-recurring.
The correct option is A.
So, the correct answer is “Option A”.

Note: We can also look at the fraction form of the decimal to under the terminating and non-terminating portion of its decimal form. If the prime factorisation of the denominator of the fraction has only 2 and 5, then it’s terminating otherwise not.