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Without actually performing the long division, state whether the following rational numbers (i) 23/(2^35^2) (ii) 129/(2^25^77^5) (iii) 6/15 (iv) 35/50

  

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Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion:

(i) 23/(2352)

(ii) 129/(225775)

(iii) 6/15

(iv) 35/50

(v) 77/210

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(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 x 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.

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