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.

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