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Question
Write the denominator of the rational number `257/5000` in the form 2m × 5n, where m, n are non-negative integers. Hence, write its decimal expansion, without actual division.
Solution
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 2m × 5n where m = 3 and n = 4 are non-negative integers.
∴ `257/5000 = 257/(2^3 xx 5^4) xx 2/2` ...[Multiplying numerator and denominator by 2]
= `514/(2^4 xx 5^4)`
= `514/(10)^4`
= `514/10000`
= 0.0514
Hence, 0.0514 is the required decimal expansion of the rational number `257/5000` and it is also a terminating decimal number.
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