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22 July, 2015

Brief notes- Number System

Number System
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 (a/b)
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 = 1/an

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