1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion:(i) 133125 (ii) 178 (iii) 64455 (iv) 151600 (v) 29343 (vi) 232352 (vii) 129225775 (viii) 615 (ix) 3550 (x) 77210

Open in App
Solution

## Theorem: Let x=pq be a rational number, such that the prime factorisation of q is of the form 2n5m, where n, m are non-negative integers. Then, x has a decimal expansion which terminates.(i) 133125Factorise the denominator, we get3125=5×5×5×5×5=55So, denominator is in form of 5m so, 133125 is terminating.(ii) 178Factorise the denominator, we get8=2×2×2=23So, denominator is in form of 2n so, 178 is terminating.(iii) 64455Factorise the denominator, we get455=5×7×13So, denominator is not in form of 2n5m so, 64455 is not terminating.(iv) 151600Factorise the denominator, we get1600=2×2×2×2×2×2×5×5=2652So, denominator is in form of 2n5m so, 151600 is terminating.(v) 29343Factorise the denominator, we get343=7×7×7=73So, denominator is not in form of 2n5m so, 29343 is not terminating.(vi) 232352Here, the denominator is in form of 2n5m so, 232352 is terminating.(vii) 129225775Here, the denominator is not in form of 2n5m so, 129225775 is not terminating.(viii) 615Divide nominator and denominator both by 3 we get 315So, denominator is in form of 5m so, 615 is terminating.(ix) 3550Divide nominator and denominator both by 5 we get 710Factorise the denominator, we get10=2×5So, denominator is in form of 2n5m so, 3550 is terminating.(x) 77210Divide nominator and denominator both by 7 we get 1130Factorise the denominator, we get30=2×3×5So, denominator is not in the form of 2n5m so 615 is not terminating.

Suggest Corrections
3
Join BYJU'S Learning Program
Related Videos
Revisiting Rational Numbers and Their Decimal Expansions
MATHEMATICS
Watch in App
Join BYJU'S Learning Program