# How to explain rational numbers, irrational numbers, and how they are different?

How to explain rational numbers, irrational numbers, and how they are different?
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Step 1 To explain: a) Rational number. b) Irrational number. c) Difference between rational number and irrational number. Step 2 a) Rational number: A Rational number is a number that can be expressed in the form of a ratio p/q, where p and q are integers and $q\ne q0$. Rational numbers are finite and has terminating or repeating decimals. Examples of rational numbers: $\frac{1}{2},\frac{7}{4},\sqrt{81},\frac{1}{100}$ etc. $\frac{3}{4}$ can be represented as 0.75 which is a terminating decimal. $\frac{2}{3}$ can be represented as 0.6666 .... which is a repeating decimal. Step 3 b) Irrational number: An irrational numbers is a number that is not rational. Irrational numbers cannot be expressed as a fraction with integer values in the numerator and denominator. Irrational numbers are infinite and has non - terminating and non-repeating terms. When an irrational number is expressed in decimal form, it goes on forever without repeating. But both the numbers are real numbers and can be represented in a number line. Examples of irrational numbers: $\frac{\sqrt{3}}{2},\pi ,0.131331333\dots .,5+\sqrt{3}$ Step 4 c) Difference between rational number and irrational number: