Pawan Prajapati
Solutions:
Note: If the denominator has only factors of 2 and 5 or in the form of 2m ×5n then it has terminating decimal expansion.
If the denominator has factors other than 2 and 5 then it has a non-terminating decimal expansion.
(i) 13/3125
Factorizing the denominator, we get,
3125 = 5 × 5 × 5 = 55
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 = 23
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 = 2652
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 = 73 Since, the denominator is not in the form of 2m × 5n thus 29/343 has a non-terminating decimal expansion.
(vi)23/(2352)
Clearly, the denominator is in the form of 2m × 5n.
Hence, 23/ (2352) has a terminating decimal expansion.
(vii) 129/(225775)
As you can see, the denominator is not in the form of 2m × 5n.
Hence, 129/ (225775) 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.
