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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?

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

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When we measure a length with scale or any other instrument, we only obtain an approximate rational value. We never obtain an exact value.
For this reason, we cannot say that either c or d is irrational.
Therefore, the fraction  $\frac{c}{d}$  is irrational. Hence, the value of $\pi$ is approximately equal to $\frac{22}{7} = 3.142857....$

Therefore, $\pi$ is irrational.

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