Classify the following numbers as rational or irrational :
(i) 23
(ii) 225
(iv) 7.478478...
(v) 1.101001000100001...
(iii) 0.3796
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Answers
Rational numbers:
The numbers which can expressed in the form of p/q, where p, q integers and q≠0, are known as rational numbers.
The collection of rational numbers is denoted by Q.
Irrational numbers:
The numbers which cannot be expressed in the form p/q, where p & q both are integers and q≠0 are called irrational numbers. e.g √2, √ 3, π e.t.c
On dividing p by q, if remainder becomes zero then the decimal expansion is terminating and if remainder never become zero and Set of digits repeats periodically then the decimal expansion is non terminating repeating. It is also known as non terminating recurring decimal expansion.
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Solution:
(i) √23 = 4.79583152331…
Since the number is non-terminating non-recurring decimal expansion.
Hence, it is an irrational number.
(ii) √225 = 15 = 15/1
Since the number is rational number as it can represented in p/qform.
(iii) 0.3796
Since the number has terminating decimal expansion.
Hence, it is an rational number.
(iv) 7.478478….. = 7.478
478 is repeating continuously so it has non terminating repeating (recurring ) decimal expansion
Hence, it is a rational number.
(v) 1.101001000100001…
Since the number is non-terminating non-repeating.
Hence, it is an irrational number.
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