NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 1: Real Numbers - Exercise 1.1 - Multiple Choice Questions
Question 10

Question. 10

The decimal expansion of the rational number \(\dfrac{14587}{1250}\) will terminate after:

(A)

one decimal place

(B)

two decimal places

(C)

three decimal places

(D)

four decimal places

First, factorize the denominator: \(1250 = 2 \times 5^4\).

Since the denominator is of the form \(2^m5^n\), the decimal expansion will terminate.

The number of decimal places equals the higher of the powers of 2 or 5 in the denominator.

Here, we have \(m = 1\) and \(n = 4\). The maximum is 4.

Therefore, the decimal expansion will terminate after 4 decimal places.