Write the denominator of the rational number 257/5000.

Write the denominator of the rational number 257/5000 in the form 2^m × 5ⁿ where m, n is non-negative integers. Hence, write its decimal expansion on without actual division.

Solution:

Given:
The fraction 257/5000
Since the denominator is 5000,
The factors for 5000 are:

5000 = 2 × 2 × 2 × 5 × 5 × 5 × 5
= 2³ × 5⁴
257/5000 = 257/(2³ × 5⁴)
It is a terminating decimal.
So,
Let us multiply both numerator and denominator by 2, we get
257/5000 = (257 × 2) / (5000 × 2)
= 514/10000
= 0.0514

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