All numbers can be classified as follows:

**Natural numbers**

All countable numbers are called natural numbers. They are denoted by N.

N = {1, 2, 3, 4…………………. ∞}**Whole numbers**

When zero is included in the set of natural numbers, they are called whole numbers. They are denoted by W.

W = {0, 1, 2, 3, 4……………… ∞}

**Integers**

The integers are natural numbers including 0 (0, 1, 2, 3, ...) and their negatives (0, −1, −2, −3, ...). They are denoted by I.**Rational numbers**

Any number which can be expressed in the form of p/q, where p and q are integers and q ≠ 0, is called a rational number. The set of rational numbers is denoted by Q.

Example: 4, 4/5, -5/8, 1/3, 2.74 etc.**Fractions**

A fraction denotes a part or parts of a unit. The following are different types of fractions.

(a) Proper fractions – Fractions whose numerators are less than its denominator,

Example: 2/3, 4/5

(b) Improper fractions – Fractions whose numerators are greater than its denominator,

Example: 7/3

(c) Mixed fractions – These fractions have 2 parts – an integer part and a fractional part,

Example: 4½

(d) Decimal fractions

Fractions in which the denominators are powers of ten are called decimal fractions.**Recurring decimals**

If in a decimal fraction, a figure or a set of figures is repeated continuously, then such a number is called a recurring decimal.

Example:

a) 1/3 = 0.333333…. = 0.33

b) 22/7 = 3.142857142857 = 3.142857

If all the figures after the decimal point repeat themselves then it is called a pure recurring decimal. If only some figures repeat and others don’t, then it is called a mixed recurring decimal.**Irrational numbers**

Any number which cannot be expressed in the form of p/q, where p and q are integers and q ≠ 0, is called an irrational number. Set of irrational numbers is denoted by Q'. They are generally the non-terminating and non-recurring decimal fractions.

Example: √3, π, e etc.**Real numbers**

Set of numbers which include both rational and irrational numbers is called real numbers. The set of real numbers is denoted by R. R = Q U Q'