Question

The number 0.211211121111211111…… is a
A. Terminating decimal
B. Non-terminating repeating decimal
C. Non-terminating and non- repeating decimal
D. None of these

Answer 1

Hint: First of all find out whether the number is ending after the decimal point. If the number is ending, it is known as the terminating number. If the number is not ending, it is known as non-terminating. Next, observe whether the same numbers are being repeated or not .

Complete step-by-step answer:

From the given number, we can observe that the number is not ending after the decimal point.
The numbers which go on and do not end are known as non-terminating decimals.
Next, we will see if the number is repeating or not.
The number of 1’s after each 2 is different after the decimal point.
The first number that is after decimal is 211 which is then followed by 2111, then 21111 and so on.
We can observe the same number is not getting repeated, moreover, it is following a pattern.
Since, the same number are not repeating, the given number is non repeating.
Hence, we conclude that the decimal, 0.211211121111.......... is non terminating and non-repeating.
The numbers which have non terminating and non-repeating decimals are known as irrational numbers.
Hence, option C is correct.

Note: In this question, many students make mistakes by neglecting the number of times 1 is getting repeated after each 2. The numbers which have non terminating and non repeating decimals are known as irrational numbers. The repeating decimals or terminating decimals can be expressed as rational numbers.