Question

Write the denominator of rational number 257/5000 in the form of 2^m ×5^n

Answer 1

Answer:

See below

Explanation:

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.

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Answer 2

Answer:

Factors of denominator are 5^4×2^3