Solutions:

Note: If the denominator has just factors of 2 and 5 or as 2m ×5n then it has ending decimal extension.

On the off chance that the denominator has factors other than 2 and 5, it has a non-ending decimal extension.

(I) 13/3125

Factorizing the denominator, we get,

3125 = 5 × 5 × 5 = 55

Since, the denominator has just 5 as its factor, 13/3125 has an ending decimal development.

(ii) 17/8

Factorizing the denominator, we get,

8 = 2×2×2 = 23

Since, the denominator has just 2 as its factor, 17/8 has an ending decimal development.

(iii) 64/455

Factorizing the denominator, we get,

455 = 5×7×13

Since, the denominator isn’t as 2m × 5n, consequently 64/455 has a non-ending decimal development.

(iv) 15/1600

Factorizing the denominator, we get,

1600 = 2652

Since, the denominator is as 2m × 5n, along these lines 15/1600 has an ending decimal extension.

(v) 29/343

Factorizing the denominator, we get,

343 = 7×7×7 = 73 Since, the denominator isn’t as 2m × 5n along these lines 29/343 has a non-ending decimal extension.

(vi)23/(2352)

Obviously, the denominator is as 2m × 5n.

Thus, 23/(2352) has an ending decimal extension.

(vii) 129/(225775)

As should be obvious, the denominator isn’t as 2m × 5n.

Thus, 129/(225775) has a non-ending decimal extension.

(viii) 6/15

6/15 = 2/5

Since, the denominator has just 5 as its factor, along these lines, 6/15 has an ending decimal extension.

(ix) 35/50

35/50 = 7/10

Factorizing the denominator, we get,

10 = 2 5

Since, the denominator is as 2m × 5n subsequently, 35/50 has an ending decimal extension.

(x) 77/210

77/210 = (7× 11)/(30 × 7) = 11/30

Factorizing the denominator, we get,

30 = 2 × 3 × 5

As should be obvious, the denominator isn’t as 2m × 5n .Hence, 77/210 has a non-ending decimal extension.