GMAT number system is a critical chapter for all aspiring gmatters. On an average about 5-7 questions on number system will be asked during the GMAT CAT.So please go through the definitions before cracking the problems

Whole Numbers :Whole Number includes all the numbers in the positive coordinates including 0.Let us represent the whole number by W,then

  W = {0,1,2,3....}

Positive Numbers/Natural Numbers:All numbers in the positive coordinate greater than 0 represents Positive numbers or are termed as natural numbers.If positive number is represented by P then

P = {1,2,3,4,5}

Note that 0 is neither positive nor negative.

Integers : Set of whole numbers and negative numbers constitute Integers and can be represented on the number line as follows

The distance between any two points say between -9 and -4 is calculated by subtracting the lower value from higher value.

Distance(-9,-4) = -4-(-9)=5

Absolute Value : The distance of the number from 0 (Zero) is represented by the absolute value( |X| )

Absolute value of -4 ( |-4| ) = 0-(-4) = 4

Rational Numbers : A number of the form p/q where q#0 is called a rational number.

For example 5/6 is a rational number . 5/0  is undefined and doesn't satisfy the rationality condition mention above.

A rational number can result in an integer ( 6/2=3) or a decimal fraction (5/6=0.833333...)

Decimal Fractions : There are two types of decimal fractions :

  a) Terminating Decimal Fraction : Like 6/5 = 1.2 Note that the decimal terminates after 2

  b) Non-Terminating Decimal Fraction : Like 5/6 = 0.833333... The decimal does not terminate

Non-Terminating Decimal Fraction : There are two types of non-terminating decimal fractions

   a) Non-Terminating Recurring : For example 5/6=0.833333.. is a non-terminating recurring decimal fraction 

       Note that 3 is recurring to infinity

   b) Non-Terminating Non-Recurring : For example 3.316624790355 is a non-terminating non-recurring decimal 

        fraction 

Irrational Numbers : Any number that cannot be represented in the form p/q where q # 0 is called an irrational number

Most common irrational numbes are square roots, cube roots and logarithms ex sqrt(2) and log(8) etc

Real Numbers : Set of rational and irrational numbers are called Real numbers

                                                           Real Number

                                                                  | 

                                    Rational Number         +           Irrational Number

                                              |              

                             Integer        +              Fractions

                                  |                               |

                           Negative + Positive           Decimal

                                                                   | 

                                                   Terminating + Non-Terminating

                                                                    |

                                          Non-terminating recurring + Non-terminating Non-recurring