Key Points - Number Systems

Rational Numbers
Irrational Numbers
Real Numbers and their Decimal Expansions
Operations on Real Numbers
Laws of Exponents for Real Numbers

- Natural numbers are - 1. 2. 3. ……………. denoted by N.
Whole numbers are - 0. 1. 2. 3. ……………… denoted by W.
Integers - ……. -3. -2. -1. 0. 1. 2. 3. ……………… denoted by Z.
Rational numbers - All the numbers which can be written in the form r / s p / q. are called  rational numbers where p and q are integers.
Irrational numbers - A number s is called irrational. if it cannot be written in the form p / q
-  where p and q are integers and
The decimal expansion of a rational number is either terminating or non-terminating recurring. Thus we say that a number whose decimal expansion is either terminating or nonterminating recurring is a rational number.
The decimal expansion of a irrational number is non terminating non-recurring.
All the rational numbers and irrational numbers taken together.
Make a collection of real number.
A real no is either rational or irrational.
If r is rational and s is irrational then r+s. r–s. r.s are always irrational numbers but r/s may be rational or irrational.
Every irrational number can be represented on a number line using Pythagoras theorem.
Rationalization means to remove square root from the denominator.
3+ 5
1 to remove we will multiply both numerator & denominator by 2 its
2 a± b rationalization factor a ? b