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

Solution:

We know that

Denominator of the rational number 257/5000 is 5000.

Factors of 5000 = 2 × 2 × 2 × 5 × 5 × 5 × 5

= (2)³ × (5)⁴

which is of the type 2^m × 5ⁿ.

m, n are non-negative integers.

257/5000 = 257/ (2)³ × (5)⁴ × 2/2.

= 514/(2)⁴ × (5)⁴

= 514/(10)⁴

= 514/10000

= 0.0514

Therefore, 0.0514 is the required decimal expansion

✦ Try This: Write the denominator of the rational number 19/256 in the form 2^m × 5ⁿ, where m, n are non-negative integers. Hence, write its decimal expansion, without actual division

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 1

NCERT Exemplar Class 10 Maths Exercise 1.3 Problem 13

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

Summary:

The denominator of the rational number 257/ 5000 in the form 2^m × 5ⁿ where m, n are non-negative integersis 514/(2)⁴ × (5)⁴ i.e . 0.0514 is the required decimal expansion

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