Look at the several examples of rational numbers in the form p/q (q ≠ 0), where p and q are integers with no common factors other than 1 and having terminating decimal representations (expansions). Can you guess what property q must satisfy?

Solution:

We shall look at some examples of rational numbers in the form of p/q (q ≠ 0), where their decimal representations are terminating.

2/5 = 0.4

3/100 = 0.03

27/16 = 1.6875

33/50 = 0.66

Let's observe the denominators of the above rational numbers.

2/5 = 2 / (2⁰ × 5¹)

3/100 = 3 / (2² × 5²)

27/16 = 27 / (2⁴ × 5⁰)

33/50 = 33 / (2¹ × 5²)

We observe that the denominators of the above rational numbers are in the form of 2^a × 5^b, where a and b are whole numbers.

Hence if q is in the form 2^a × 5^b then p/q is a terminating decimal.

☛ Check: Class 9 Maths NCERT Solutions for Chapter 1

Video Solution:

Look at the several examples of rational numbers in the form p/q (q ≠ 0), where p and q are integers with no common factors other than 1 and having terminating decimal representations (expansions). Can you guess what property q must satisfy?

NCERT Solutions Class 9 Maths Chapter 1 Exercise 1.3 Question 6:

Summary:

The property that q must satisfy to be a terminating decimal in the form of p/q (q ≠ 0), where p and q are integers with no common factors other than 1 is that q must be in the form of 2^a × 5^b  where a and b are whole numbers.

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