Question

$\pi rational number or irrational number$
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Answer 1

$\bold{\pi}$ is an irrational number and not a rational number.

Many of us is confused with it. But $\pi$ is always an irrational number. This's because when we divide the decimal expansion is 3.1415926535......

As we can see here, it's decimal expansion is non - terminating and non - recurring.

Non - terminating means non - stoping. The dots in 3.1415926535...... are representing that the number is never ending.

As we can see that, the decimal expansion is not repeating. Every second number is changing.

Non - recurring means non - repeating.

So, $\pi$ is not a rational number. It's an irrational number.

So, $\pi$ can be expressed in the form of $\frac{p}{q}$ where p and q are integers and q $\neq$ 0.

But $\frac{22}{7}$ is a rational number as its decimal expansion is non - terminating and recurring.

Answer 2

Answer:

Proof that π is irrational. In the 1760s, Johann Heinrich Lambert proved that the number π (pi) is irrational: that is, it cannot be expressed as a fraction a/b, where a is an integer and b is a non-zero integer. ... Another proof, which is a simplification of Lambert's proof, is due to Miklós Laczkovich.