Without actually performing the long division, find if 987/10500 will have terminating or non-terminating (repeating) decimal expansion. Give reasons for your answer

Solution:

The given number is 987/10500

Let us determine the HCF of 987 and 10500.

987 = 3 × 7 × 47

10500 = 2 × 2 × 3 × 5 × 5 × 5 × 7

HCF of (987, 10500) = 3 × 7

HCF of (987, 10500) = 21.

By dividing the numerator and denominator with HCF,

= (987 / 21) / (10500 / 21)

= 47 / 500

987 / 10500 = 47 / 500.

The denominator 500 can be written as

500 = 2² × 5³

2 and 5 are the factors.

If a fraction contains no other prime factors other than 2 and 5, it can be written in the lowest terms as the terminating decimal.

Therefore, 987/10500 is terminating decimal.

✦ Try This: Without actually performing the long division, find if 935/10500 will have terminating or non-terminating (repeating) decimal expansion. Give reasons for your answer

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

NCERT Exemplar Class 10 Maths Exercise 1.2 Problem 9

Without actually performing the long division, find if 987/10500 will have terminating or non-terminating (repeating) decimal expansion. Give reasons for your answer

Summary:

Without actually performing the long division, 987/10500 will have terminating decimal expansion

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