Question

please answer it 9th class question of math​

Answer 1

a number which can neither be expressed as a terminating decimal nor as repeating decimal, is called irrational number.

the number from of p/q where p, q integer q does not equal to 0

0.01001000100001

.

Answer 2

$\boxed{\bold{Irrational\:numbers:}}$

A number which cannot be expressed in the form of $\frac{p}{q}$, where p and q are integers and q ≠ 0.

For example : - $\sqrt{2}, \sqrt{3}, \sqrt{5}, \pi$ etc.

It's just opposite of rational numbers.

$\boxed{\bold{Rational\:numbers:}}$

Rational numbers are the numbers which can be expressed in the form of $\frac{p}{q}$ where p and q are integers and q ≠ 0.

Rational numbers in terms of its decimal expansion are of two types :

(i) terminating

(ii) non - terminating and recurring (repeating)

But as we talk 'bout irrational numbers, they are non - terminating and non - recurring.

For example : - $\sqrt{2}$ = 1.414213562373.....

As we can see here, the decimal expansion of $\sqrt{2}$ is non - terminating and non - recurring.

But rational number's decimal expansion is either terminating or non - terminating and recurring.

The below example will give you more clarity.

Eg : - 0.212121......

Here, a number or a block of number is repeating.

But we can express 0.212121.... in the form of $\frac{p}{q}$. How? See below.

Let x be the number 0.212121....

Then multiplying 10 on both sides.

10x = 21.2121....

10x = 21 + 0.212121......

10x = 21 + x (as x = 0.212121.....)

10x = 21 + x

10x - x = 21

9x = 21

x = $\frac{21}{9}$

x = $\frac{\cancel{21}}{\cancel{9}}$

x = $\frac{7}{3}$

Here, 0.212121... is expressed in the form of $\frac{p}{q}$ where, p and q are integers and q ≠ 0.

Here, both the numbers 7 and 3 are integers and 3 ≠ 0.

A rational number can be expressed in $\frac{p}{q}$ but an irrational number cannot.