1) A number r is called a rational number if it can be written in the form of p/q
, q ≠ 0 and p and q are integers.
2) There are infinitely many rational numbers between any two rational numbers.
3) A numbers is called an irrational numbers if it cannot be expressed in the form of p/ q, where p and q are integers and representation q≠0 (or which is not a rational numbers e.g.Ö2,Ö3…..)
4) The decimal expansion of a rational numbers is either terminating or non terminating recurring .
5) The decimal expansion of an irrational numbers is non- terminating and non -repeating.
6) Every point on a line represents a real number.
7) The sum, difference, multiplication and division of two rational numbers is a rational number but the same is not true in case of irrational numbers.
8) To rationalize the denominator of 1/(a + Öb)
, we multiply and divide by (a - Öb).
9) For positive real numbers a and b,
a) Öa . Öb = Öab
b) Öa ÷ Öb =Ö
c) (Öa + Öb)2 = a + 2Öab + b
d) (Öa + Öb) (Öa - Öb) = a – b
10) If a>0 be a real number and p and q are rational numbers, then
a) ap . aq = a p+q
b) ap ÷ aq = a p-q
c) ap . bp = abp
d) (ap )q= a pq
e) a0 = 1
f) a-n =