Classify the following numbers as rational or irrational: (i) √23 (ii) √225 (iii) 0.3796 (iv) 7.478478... (v) 1.101001000100001... (vi) 345.0 ̅4 ̅5 ̅6

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Rational numbers are in the form c, q ≠ 0, and p and q are integers. (i) is an irrational number , as it is not a perfect square so it cannot be written in the form , q ≠ 0. (ii) = = 15 = , As it can be written in the form , q ≠ 0. ∴ is a rational number . (iii) 0.3796 = Since, the decimal expansion is terminating decimal. ∴ 0.3796 is a rational number . (iv) 7.478478 Let x = 7.478478 Since there is three repeating digit after decimal point, Multiplying both sides by 1000, we get 1000x = 7478.478478... Subtracting (i) from (ii) we get, 999x = 7471 x = ∴ It is non terminating , repeating rational number . (v) 1.101001000100001... Since number of 0's are increasing between two consecutive terms as we move further , So it is non terminating, non repeating decimal. ∴ 1.101001000100001... is an irrational number. (vi) = 345.0456456... Let x = 345.0456456... Multiply both sides by 10, we get 10x = 3450.456456.. Since, after decimal there are three repeating digit: Multiply both sides by 1000, we get 10000x = 3450456.456456... Subtracting (i) from (ii) , 9990x = 3447006 x = since, it is non-terminating , repeating decimal. ∴ is a Rational number .

Mathematics

Classify the following numbers as rational or irrational: (i) √23 (ii) √225 (iii) 0.3796 (iv) 7.478478... (v) 1.101001000100001... (vi) 345.0 ̅4 ̅5 ̅6

Rational Irrational Nos

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