Brief Notes- Reveal System

Number System

1) H5N1 number   r   is   called a rational pose out if it tin flaming endure written inward the shape of p/q    , q ≠ 0 in addition to p in addition to q are integers.

2) There are infinitely many rational numbers betwixt whatever ii rational numbers.

3) H5N1 numbers is called an irrational numbers if it cannot endure expressed   in the shape of p/ q, where p in addition to q are integers in addition to representation q≠0  (or which is non 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 in addition to non -repeating.

6)  Every betoken on a business represents a existent number.

7) The sum, difference, multiplication in addition to partition of ii rational numbers is a rational pose out simply the same is non truthful inward illustration of irrational numbers.

8) To rationalize the denominator of 1/(a + Öb), nosotros multiply in addition to dissever by  (a - Öb).

9) For positive existent numbers a in addition to 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 endure a existent pose out in addition to p in addition to q are rational numbers, then

a)     a^p . a^q = a ^p+q

b)    a^p ÷ a^q = a ^p-q

c)     a^p . b^p = ab^p

d)    (a^p )^q= a ^pq

e)     a⁰  = 1

f)      a^-n = 1/aⁿ

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