Question

Write the denominator of the rational number 257/5000 in the form 2^m×5^n where m,n are non negative integers.

Answer 1

The denominator of 257/5000 is 5000.
5000=2×2×2×5×5×5×5
5000=2³5⁴
Here, decimal expansion of 5000 is in the form of 2^m and 5^n. (m=3 and n=4). Therefore its decimal expansion will be terminating.

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Answer 2

Denominator of the rational number 257/ 5000 is 5000.
Now, 5000 = 2 × 2 × 2 × 5 × 5 × 5 × 5
= (2)^ 3 × (5)^ 4 , which is of the type 2 × 5 , (where m = 3 and n = 4 are non-negative integers.)
∴ Rational number = 257/5000
= 257/2^3×5^4 × 2/2
= 514/2^3×5^4
= 514/(10)^4
= 514/10000
= 0.0514
So, 0.0514 is the required decimal expansion of the rational 257/5000 and it is also a terminating decimal number.