Question

Without actually performing long division state whether following rational numbers have terminating or non-terminating repeating decimal expansion –

a) 111/125 b 29/343 c)9/27 d) 17/1600 e)127/2^(3 5^2 )

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Answer 1

Answer:

a. terminating decimal expansion

b. non terminating decimal expansion

c. terminating decimal expansion

d. non terminating decimal expansion

Answer 2

Answer:

☆Let x=p/q be a rational number,Such that the prime factorisation of q is of the form 2^n×5^m or 2^n or 5^m is TERMINATING,If it does not in the form 2^n×5^m it is NON-TERMINATING AND REPEATING☆

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a)111/125

=111/5^3

=111×2^3/5^3×2^3

=111×8/10^3

=888/1000

=0.888

Its Terminating.....

b)29/343

=29/7^3

Its Non-terminating and repeating.....

c)9/27

=1/3

Its Non-terminating and repeating.....

d)17/1600

=17/2^6×5^2

=17×5^4/2^6×5^2×5^4

=11250/10^6

=11250/1000000

=0.011250

Its Terminating.....

e)127/2^3×5^2

=127×5^1/2^3×5^2×5^1

=635/10^3

=635/1000

=0.635

Its Terminating.....

HOPE IT HELPS YOU.......