Concept teaser

Number Theory Level pending

We all have read that π =3.14........ And. 22/7 = 3.14...... Too. Then why π is irrational and 22/7 is rational..?

π is a constant 22/7 is not rational π is not irrational π is not equal to 22/7

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2 solutions

Chew-Seong Cheong
Apr 24, 2015

π 22 7 \boxed{\pi \ne \frac{22}{7}} . 22 7 \frac{22}{7} is only an approximation of π \pi and π \pi is irrational while 22 7 \frac{22}{7} is rational.

From Python, the value of π = 3.141592653589793 \pi = 3.141592653589793 and 22 7 = 3.142857142857143 π 22 7 \frac{22}{7} = 3.142857142857143\quad \Rightarrow \pi \approx \frac{22}{7} .

But we can say that π \pi is a constant whose value is 3.1428571... 3.1428571 ... Further its value does not vary.

Samrit Pramanik - 6 years, 1 month ago
Shoaib Ur Rehman
Apr 24, 2015

Actually π is equal to 3.14159.... And cannot be expressed as a rational number.. But 22/7 is the nearest possible rational value say approximately equal to π and so is used by students of primary classes.

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