Classify the following numbers into two groups and label each group correctly.

(1) (2) 0.31045693…

(3) (4)

(5) (6) 0.1010010001…

We can classify the above given decimals into 3 groups. Terminating and Non-Terminating numbers.

i) Recurring and Non-Recurring numbers.

ii) Rational and Irrational numbers.

First, we should know what is terminating and non-terminating.

i. Terminating Numbers : The numbers which have an end (or) which have countable digits(finite).

Eg. 10.0123789456, 2.5896374

ii. Non-Terminating Numbers: The number which doesn’t has an end (or) They consists of uncountable digits(infinity).

Eg.20.15637894387…, 78.9848678898…

(Group 2): Recurring numbers: It is a decimal which has repeated set of numbers. Eg.

20.02020202…. , 46.464646464….

Non-Recurring numbers: It is a decimal which doesn’t have repeated set of numbers

Eg. 10.9848678898…., 97.852963741…

Group 3: Rational and Irrational numbers:

A number which can be written in the form of where numerator and denominators are integers except zero, then that is known as rational number.

A number which cannot be written in the form of or when numerator and denominators are not integers, then that is known as irrational numbers.