# Classify the following numbers as rational or irrational:

i) √23 ii) √225 iii) 0.3796 iv) 7.478478... v) 1.101001000100001...

**Solution:**

i) √23

√23 = √23/1 = p/q, but p is not an integer.

Hence √23 is an irrational number.

ii) √225

√225 = 15/1 = p/q, where p and q are integers and q ≠ 0.

Hence √225 is a rational number.

iii) 0.3796

0.3796 is a rational number because it is a terminating decimal number.

iv) 7.478478...

7.478478... is a rational number as it is a non-terminating recurring decimal i.e, the block of numbers 478 is repeating.

v) 1.101001000100001 . . . .

It is an irrational number because it is a non-terminating and non-recurring decimal.

**☛ Check: **NCERT Solutions for Class 9 Maths Chapter 1

**Video Solution:**

## Classify the following numbers as rational or irrational: i) √23 ii) √225 iii) 0.3796 iv) 7.478478... v) 1.101001000100001...

NCERT Solutions Class 9 Maths Chapter 1 Exercise 1.3 Question 9

**Summary:**

√23, 1.101001000100001... are irrational numbers whereas √225, 0.3796, and 7.478478... are rational numbers.

**☛ Related Questions:**

- What can be the maximum number of digits be in the repeating block of digits in the decimal expansion of 1/17? Perform the division to check your answer.
- 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 representation (expansions). Can you guess what property q must satisfy?
- Write three numbers whose decimal expansions are non terminating and non-recurring.
- Find three irrational numbers between the rational numbers 5/7 and 9/11.