Recall, $$\pi$$ is defined as the ratio of the circumference(say c) of a circle to its diameter(say d). That is, $$\pi=\displaystyle\frac{c}{d}$$. This seems to contradict the fact that $$\pi$$ is irrational. How will you resolve this contradiction?
Here,
π=227π=227
Now, it is in the form of pqpq , which is a rational number, but this is an approximate value of ππ .
If you divide 2222 by 77 , the quotient (3.14⋯)(3.14⋯) is a non-terminating number i.e. it is irrational.
Approximate fractions include (in order of increasing accuracy)
227,333106,355113,⋯227,333106,355113,⋯
If we divide anyone of these we get, the quotient (3.14⋯)(3.14⋯) is a non-terminating number. i.e. it is irrational.
So,
There is no contradiction as either cc or dd irrational and
hence ππ is a irrational number.
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