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# Recall, π is defined as the ratio of the circumference (say c) of a circle to its diameter (say d). That is, π = c/d. This seems to contradict the fact that π is irrational. How will you resolve this contradiction?

**Solution:**

π is defined as the ratio of the circumference (say c) of a circle to its diameter (say d), that is, π = c/d. Hence, we see that π is a rational number as it is expressed in the form of p/q. But, we know that π is an irrational number. Let's resolve the contradiction.

Writing π as 22/7 is only an approximated value and so we can’t conclude that it is in the form of a rational number. In fact, the value of π is calculated as the non-terminating, non-recurring decimal number as π = 3.14159... whereas, if we calculate the value of 22/7, it gives 3.142857 and hence π is not exactly equal to 22/7.

In conclusion, π is an irrational number.

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

**Video Solution:**

## Recall, π is defined as the ratio of the circumference (say c) of a circle to its diameter (say d). That is, π = c/d. This seems to contradict the fact that π is irrational. How will you resolve this contradiction?

NCERT Solutions Class 9 Maths Chapter 1 Exercise 1.5 Question 3:

**Summary:**

Writing π as 22/7 is only an approximated value and so we can’t conclude that it is in the form of a rational number. In conclusion, π is an irrational number.

**☛ Related Questions:**

- Recall, π is defined as the ratio of circumference (say c) of a circle to its diameter (say d). That is, π = c/d. This seems to contradict the fact that π is irrational. How will you resolve this contradiction?
- Represent √9.3 on the number line.
- Rationalize the denominators of the following: i) 1/√7 ii) 1/(√7 - √6) iii) 1/(√5 + √2) iv) 1/(√7 - 2)

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