Without actual division, state whether the following rational numbers are terminating or non-terminating, repeating decimals.(i) 16/125 (ii) 25/32 (iii) 100/81 (iv) 41/75
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heya...
Here is your answer...
1) 16 / 125 = 2×8/5^3 = 2×2×2×2/5^3
so it is a terminating decimal.
2) 25/32 = 5×5/2×2×2×2×2
so it is a terminating decimal.
3) 100/81 = 10^2/3^4
So it is not a terminating decimal.
4) 41/75 = 41/5×5×3
so it is a terminating decimal.
Expect 3) all are terminating decimals because there denominator is a multiple of 2 or 5.
It may help you...☺☺
Here is your answer...
1) 16 / 125 = 2×8/5^3 = 2×2×2×2/5^3
so it is a terminating decimal.
2) 25/32 = 5×5/2×2×2×2×2
so it is a terminating decimal.
3) 100/81 = 10^2/3^4
So it is not a terminating decimal.
4) 41/75 = 41/5×5×3
so it is a terminating decimal.
Expect 3) all are terminating decimals because there denominator is a multiple of 2 or 5.
It may help you...☺☺
Krishnagupta11:
hlw
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