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 $q \neq q 0$ . 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: $\frac{\sqrt{3}}{2}, π, 0.131331333 \dots ., 5 + \sqrt{3}$ Step 4 c) Difference between rational number and irrational number: $\begin{array}{cc} R a t i o n a l n u m b e r & I r r a t i o n a l n u m b e r \\ I t i s e x p r e s s e d i n t h e r a t i o, w h e r e b o t h n u m e r a t o r a n d d e n o m i n a t o r a r e t h e w h o l e n u m b e r s & I t i s i m p o s s i b l e t o e x p r e s s i r r a t i o n a l n u m b e r s a s f r a c t i o n s o r i n a r a t i o o f t w o i n t e g e r s \\ I t i n c l u d e s p e r f e c t s q u a r e s & I t i n c l u d e s s u r d s (w e c a n^{'} t s i m p l i f y a n u m b e r t o r e m o v e a s q u a r e r o o t) \\ T h e d e c i m a l e x p a n s i o n f o r r a t i o n a l n u m b e r e x e c u t e s f i n i t e o r r e c u r r i n g d e c i m a l s & H e r e, n o n - t e r m i n a t i n g a n d n o n - r e c u r r i n g d e c i m a l s a r e e x e c u t e d \end{array}$

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

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