Question

9/1600,State whether given rational number have terminating decimal expansion or not and if it has terminating decimal expansion, find it.

Answer 1

In the attachment I have answered this problem.

Concept:

Rational numbers of the form

p/(2^m×5^n) will have terminating

decimal expansion

See the attachment for detailed solution

Answer 2

If the factors of denominator of the given rational number is of form 2ⁿ 5^m ,where n and m are non negative integers, then the decimal expansion of the rational number is terminating otherwise non terminating recurring.
SOLUTION:
9/1600
9 / (2^6× 5²)
Here, the factors of the denominator 1600 are 2^6 5² which is in the form 2ⁿ 5^m . It has a has terminating decimal expansion which can be expressed as
9 / (2^6× 5²)
= 9 × 5⁴ / (2^6× 5²× 5⁴)
= 9 × 5⁴ / (2^6× 5^6)
= 9 × 625/10^6
= 5625/ 1000000
= 0.005625
Hence, the decimal expansion of 9/1600 is 0.005625.
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