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in Number System by (65.5k points)

Recall, 2π is defined as the ratio of the circumference (say c) of a circle to its diameter (say d). That is, π = \(\frac{c}{d}\). This seems to contradict the fact that n is irrational. How will you resolve this contradiction ?

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There is no contradiction. When we measure a length with a scale or any other device we get quotient. 

Therefore we cannot judge whether c is a rational number of d is an irrational number. 

∴ Value of \(\frac{c}{d}\) is irratrional number. 

∴ Value of π is also irrational number.

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