Question

A number is an irrational if and only if its decimal representation is :
A. non terminating
B. non terminating and repeating
C. non terminating and non repeating
D. terminating

Answer 1

Hint: By knowing what are rational and irrational numbers and the definitions involved in them. From the definitions we can conclude that, what type of irrational that is there in the given question.

Complete step-by-step solution -
Rational number: A number is a number that can be expressed as fraction p/q of two integers, a numerator p and a non zero denominator q.
The decimal expansion of a rational number always either terminates after a finite number of digits or begins to repeat the same finite sequence of digits over and over. Moreover, any repeating or terminating decimal represents a rational number.
A real number that is not rational is called an irrational number.
According to definition of irrational number, If written in decimal notation, an irrational number would have an infinite number of digits to the right of the decimal point, without repetition . . . . . . . . . . . . . . . . . . (1)
From definition (1) we can say that the number is an irrational number if and only if its decimal representation is non terminating and non repeating.
Therefore the answer is option C.

Note: By knowing the definitions we can simply answer this type of question, Taking care while picking the options as they are confusing in the above question. Confusion arises in the terms of terminating and repeating type terms.