Question 9:
Classify the following numbers as rational or irrational:
(i) √23 (ii) √225 (iv) 0.3796
(iv) 7.478478 (v) 1.101001000100001…
Answer:
(i) √23 = 4.79583152331…
As the decimal expansion of this number is non-terminating non-recurring, therefore, it is an irrational number.
It is a rational number as it can be represented in p/q form.
(iii) 0.3796
As the decimal expansion of this number is terminating, therefore, it is a rational number.
As the decimal expansion of this number is non-terminating recurring, therefore, it is a rational number.
(v) 1.10100100010000 …
As the decimal expansion of this number is non-terminating non-repeating, therefore, it is an irrational number.
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