Question

without actually performing long division, State whether the following rational number will have a terminating decimal expansion or non terminal reapiting decimal expansion. 27/128, 231/400,245/875

...please help me in some ouestions ​

Answer 1

Answer:

27/128 - terminating

231/400 - terminating

245/875 - terminating

Explanation:

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Answer 2

Answer:

a) terminating

b) terminating

c) non terminal repeating

Explanation:

for the terminating condition: a/b

where,"b" the denominator should have factors be in the form of either 2^m or 5^n or even both simultaneously.

and since a) 27/128

denominator factors(128)=2^7, therefore is terminating,

similarly,

b) denominator factors (400)=2^2×5^2×2^2, therefore it's also terminating.

but,

c) denominator factors (875)=5^3×7,so according to the condition 7 should not be there and hence it's non terminating, repeating