Rational Numbers :
If p is any integer and q is any nonzero integer, then the numbers of the form p/q is said to be rational number.Examples : 1) 0, 1, 2, 3, 4, .... all these numbers are rational numbers because these numbers can be
written as 0/1, 1/1, 2/1, 3/1, 4/1, ...... .
2) All natural numbers are rational numbers.
3) All integers are rational numbers.
The Decimal form of a rational numbers
1) Terminating form 2) Non termination form : Two types : i) recurring ii) non recurring
Examples :
No matter how many zeros we write after the last digit in terminating decimal fraction, the number obtained has the same value as the original number.
Example : 8.54, 8.540, 8.5400, 8.54000 all are equivalent.
The decimal form of every rational number can be written in the non-terminating recurring form.
Terminating decimal form examples Non terminating recurring form examples
1) 0.16 1) 0.160
2) 4.439 2) 4.4390
3) 10.605 3) 10.6050
Every number in non-terminating recurring decimal form is a rational number.
A number whose decimal form is non terminating but is recurring is a rational number.
Irrational Numbers :
A number which is non terminating but non recurring are called irrational numbers.
Examples: 1) \/2 = 1.414213562373695048801687242097.....
2) \/3 = 1.7320508075688772935274463415059......
The square root of the numbers that are not perfect squares are irrational numbers.
Examples : \/2, \/3, \/5, \/7, \/11, \/13, .....
Real numbers :
The collection of rational numbers and irrational numbers is called real numbers collection.
Examples : 1.57, 2, 34, 10.10, 1.10100100010000....., \/7, \/25, \/16