Hg
Name: Class 9
___________________________________________________________________________________________________________________________________
___________________________________________________________________________________________________________________________________
The Hg Classes (8
th
to 12
th
) By: Er Hershit Goyal (B.Tech. IIT BHU), 134-SF, Woodstock Floors, Nirvana Country, Sector 50, GURUGRAM +91 9599697178.
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Number System – Notes
1. A number r is called a rational number if it can be written in the from
, where p and q are integers and
q ≠ 0. The decimal representation of a rational number is either terminating or recurring. e.g.
,
,
,
, 0.75, 0.5, 7.24, -1.123, -3.333333… or -3.
, 2.575757…. or 2.
etc.
2. A number s is called an irrational number if it cannot be written in the form
, where p and q are
integers and q ≠ 0. The decimal representation of an irrational number is neither terminating nor
recurring. It goes on and on… e.g. pi or ∏,
,
,
,
, 3.14159…, 1.181181118…. etc.
3. There is a unique real number corresponding to
every point on the number line and vice-versa.
4. Operations on Rational and Irrational numbers:
Rational (+ - * /) Rational = Rational
Rational (+ - * /) Irrational = Irrational
Irrational (+ - * /) Irrational = can be either
irrational or rational
5. Rationalization is the process of removing the irrational part from a given number.
To rationalize the denominator of
, we multiply both numerator and denominator by
.
6. Laws of exponents:
i. (x
a
)
b
= x
ab
Power to the Power, Powers are multiplied.
ii. x
a
.x
b
= x
a+b
In multiplication case, same base Powers are added.
iii.
= x
a-b
In division case, same base Powers are subtracted.
iv. x
0
= 1 Anything raised to the power zero is one.
iv. x
a
.y
a
= (xy)
a
v. x
-m
=
7. Real Number line showing all types of numbers:
