Why Pi is Irrational and 22 7 is Rational? (2024)

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Rational Numbers

Why Pi is Irr...

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Solution

Rational and irrational numbers:
Rational numbers are those numbers that can be written as a fraction of two numbers where the denominator is not zero.
Irrational numbers are those numbers that cannot be written as a fraction of two numbers.
The approximate value of $π$ is $3.14159 . . .$ which is a non-terminating and non-repeating decimal. This cannot be written as a fraction of two whole numbers.
The number $\frac{22}{7}$ is an approximation of the value of $π$ that is used for easier calculations. Since $22$ and $7$ are two whole numbers that are written in the form of a fraction, it is a rational number,

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Irrational Numbers - Pre-Algebra [Solved] Is 4 an irrational number?Rational and Irrational Numbers (Definition & Examples)Proof: √2 is irrational | Algebra (video) | Khan Academy

Similar questions

Q.

Which of the following is a true statement ?

(a) (\pi\) and 227 are both rationals.

(b) π and 227 are both irrationals.

(c) π is rational and 227 is irrational.

(d) π is irrational and 227 is rational.

Q. Which of the following is a true statment?
(a) $π and \frac{22}{7}$ are both rationals
(b) $π and \frac{22}{7}$ are both irrationals
(c) $π$ is rational and $\frac{22}{7}$ is irrational
(d) $π$ is irrational and $\frac{22}{7}$ is rational

Rational and Irrational Numbers - Terminating and Repeating Decimals

Q.

State, in each case, whether the given statement is true or false.

(i) The sum of two rational numbers is rational.

(ii) The sum of two irrational numbers is irrational.

(iii) The product of two rational numbers is rational.

(iv) The product of two irrational numbers is irrational.

(v) The sum of a rational number and an irrational number is irrational.

(vi) The product of a nonzero rational number and an irrational number is a rational number.

(vii) Every real number is rational.

(viii) Every real number is either rational or irrational.

(ix) π is irrational and 227 is rational.

Q.

Justify why 22/7 is rational but π is irrational

Q.

227 is a rational number but pi is an irrational number. Comment on this. [3 MARKS]

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