Foundation
Mathematics Foundation
Properties of Real Number
Irrational Number
Rational Numbers
Question
Classify the following numbers as rational or irrational:
(i) 23
(ii) 225
(iii) 0.3796
(iv) 7.478478...
(v) 1.101001000100001...
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Solution
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Solve the given expressions 

(1) 23=4.795831523..........

The decimal expansion is non terminating non recurring.

23 is a irrational number.

(2)225=15 

225 is a rational number.

(3) 0.3796 is the decimal expansion is terminating.

So 0.3796 is a rational number.

(4) 7.478478......=7.478 is the decimal expansion is non termination and recurring.

7.478478...... is a rational number.

(5) 1.101001000100001...... is the decimal expansion is non termination and non recurring. 71.101001000100001...... is a irrational number.