Question

2.56 is rational number or irrational number (give reason)

Answer 1

Rational number.

First, let us know what is a rational and and Irrational number.

$\bullet\qquad\mathbb{RATIONAL \ NUMBERS}$

A number which can be expressed as $\rm \dfrac{a}{b},$ where 'a' and 'b' both are integers and $\rm b \neq 0,$ is a rational number.

$\bullet\qquad\mathbb{IRRATIONAL \ NUMBER}$

• The square roots, cube roots, etc., of natural numbers are irrational numbers; if their exact values cannot be obtained.
• $\rm\sqrt{m} \ is \ irrational, \ if \ exact \ square \ root$ of $\rm m$ doesn't exist.
• A non-terminating and non-recurring decimal is an irrational number.
• Example :- 0.42434445 ............. and so on.
• Special numbers like $\pi \ and \ e$ are irrational numbers as their exact value can't be obtained.

__________________________________

Here,

2.56 is a rational number as it is completely satisfying all the properties of a rational number. It can be expressed as $\rm \dfrac{256}{100}$

$\rm \dfrac{256}{100}$ is expressed in the form of a/b where b ≠ 0 and both are integers.

Therefore, 2.56 is a Rational number.