We know that a rational number is a number that can be written in the form of \frac{p}{q} where p, q \in Z and q ≠ 0. The numbers 25, 3.765, 4.5, etc., are rational numbers. can be reduced to the form \frac{p}{q} where p, q Z, and q ≠ 0 because \sqrt{25}=5
Examples of rational numbers:
i) 0.26= is a rational number.
ii) 3.6666… is a recurring decimal, it is a rational number.
iii) 5.333…is a rational number.
iv) 0.142857142857… is a rational number.
What is Irrational Numbers:-
Irrational numbers are those numbers which cannot be put into the form of \frac{p}{q} where p, q \in Z and q ≠ 0. The numbers \sqrt{7},\sqrt{11},\sqrt{\frac{5}{16}} are irrational numbers.
Examples of Irrational numbers:
v) 0.0100100010100000001 … is a non-terminating, non-periodic decimal, so it is an irrational number.
vi) 287.12116283873112373573 … is also an irrational number.
vii) 1.4142135 … is an irrational number.
viii) 7.3205080 … is an irrational number.
ix) 1.709975947 … is an irrational number
. x) 3.141592654… is an important irrational number called it (Pi) which denotes the constant ratio of the circumference of any circle to the length of its diameter i.e.,
\pi = \frac{circumference \: of \: circle}{ diameter \: of\: circle}
An approximate value of \pi is \frac{22}{7} ,a better approximation is \frac{355}{113}and a still better approximation is 3.14159. The value of \pi is correct to upto 5 lac decimal places has been determined with the help of computer.