Numbers

  NUMBERS

Consider a complex number. We can subdivided from complex number to whole numbers as

1.      Complex number: Real number + imaginary number

2.      Real number:  Rational number + irrational number

3.      Rational number: Integers + Decimal

v  Complex number consists of real part and imaginary part. Ex: 4+3i.The graph used to represent complex number is called argand diagram. It has Real part along abscissa and imaginary part along ordinate.

v  Real numbers consists of rational and irrational number thus the whole number line i.e. from (-∞, + ∞).

·         Rational numbers are those which are terminating or repeating. Ex 14.5869, 48, 27.333333333…….

·         Irrational numbers are those which are non-terminating and non-repeating.

Ex π (3.141592653589793….), e (2.71828182846), 2^1/2 (1.414213562373)

v  Rational numbers are subdivided into integers and decimals.

·         Decimals are those with a decimal point. Ex 0.1424, 1.414, 1.732, 20.689 etc.

§  Proper fractions are those which has numerator lesser than denominator i.e. they are lesser than 1. Ex 2/3, 7/8 etc.

§  Improper fractions are those which has numerator greater than denominator i.e. they are greater than 1. Ex 2/3, 7/8 etc.

§  Mixed fractions are those which are of form 10 1/6. The result is 61/6 (i.e. 6*10 + 1 = 61 and /6 is to be written. Thus 61/6).

The concept of mixed fraction is that it converts improper fraction to proper fraction.

·         Integers are the round figures like 5, 25, 968, -30415 etc. The positive integers are from (0, ∞) and negative integers are from (-∞, 0).

§  The positive integers if started from 0 to ∞ are said to be whole numbers.

§  The positive integers that start from 1 to ∞ are said to be natural numbers.