RATIONAL NUMBER
If there a fractional number which can be expressed in the form a/b, where a & b are integers whereas a ≠ 0 and b ≠ 0, so these numbers should be called Rational Number. Suppose the set of rational numbers is denoted by Q
a
So, Q = { -------- : a, b ∈ I , and b ≠ 0 }
b
We can say, obviously Fractions are rational numbers. For example -
5 8 9 -7 -11
------, ------, ------, ------, ------ are rational numbers.
11 35 25 17 115
We have remember that, natural numbers and integers are also rational numbers, as an example –
9 27 -25 -17
9 = -------, 27 = ------, -25 = -------, -17 = -------
1 1 1 1
Any terminating or recurring decimal can be expressed as a rational number, for example -
3313 29
3.313 = --------, 0.325 = --------, etc are rational numbers.
1000 90
Numbers such as √2, √3 & ∏ cannot be expressed as rational numbers, they are called irrational.