please answer all the questions it's argent
Answers
1)i)13/3125
Factorizing the denominator, we get,
3125 = 5 × 5 × 5 = 5^5
Since, the denominator has only 5 as its factor, 13/3125 has a terminating decimal expansion.
ii)17/8
Factorizing the denominator, we get,
8 = 2×2×2 = 2^3
Since, the denominator has only 2 as its factor, 17/8 has a terminating decimal expansion.
iii)64/455
Factorizing the denominator, we get,
455 = 5×7×13
Since, the denominator is not in the form of 2m × 5n, thus 64/455 has a non-terminating decimal expansion.
iv)15/1600
Factorizing the denominator, we get,
1600=2^6×5^2
Since, the denominator is in the form of 2m × 5n, thus 15/1600 has a terminating decimal expansion.
v)29/343
Factorizing the denominator, we get,
343 = 7×7×7 = 7^3
Since, the denominator is not in the form of 2m × 5n thus 29/343 has a non-terminating decimal expansion.
vi)23/2^3×5^2
Clearly, the denominator is in the form of 2m × 5n.
Hence,23/2^3×5^2 has a terminating decimal expansion.
vii)129/2^2×5^7×7^5
As you can see, the denominator is not in the form of 2m × 5n.
Hence,129/2^2×5^7×7^5 has a non-terminating decimal expansion.
viii)6/15
6/15 = 2/5
Since, the denominator has only 5 as its factor, thus, 6/15 has a terminating decimal expansion.
ix)35/50
35/50 = 7/10
Factorising the denominator, we get,
10=2×5
Since, the denominator is in the form of 2m × 5n thus, 35/50 has a terminating decimal expansion.
x)77/210
77/210 = (7× 11)/ (30 × 7) = 11/30
Factorising the denominator, we get,
30 = 2 × 3 × 5
As you can see, the denominator is not in the form of 2m × 5n .Hence, 77/210 has a non-terminating decimal expansion.