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.

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