# 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 / (2^{0} × 5^{1})

3/100 = 3 / (2^{2} × 5^{2})

27/16 = 27 / (2^{4} × 5^{0})

33/50 = 33 / (2^{1} × 5^{2})

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.

**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.