A number is an arithmetic value used for representing the quantity and used in making calculations. A written symbol like “3” which represents a number is known as numerals.
A number system is a writing system for denoting numbers using digits or symbols in a logical manner. The numeral system:
- Represents a useful set of numbers
- Reflects the arithmetic and algebraic structure of a number
- Provides standard representation
The different types of numbers in maths are:
(i) Natural Numbers: Natural numbers are known as counting numbers that contain the positive integers from 1 to infinity. The set of natural numbers is denoted as “N” and it includes N = {1, 2, 3, 4, 5, ……….}
(ii) Whole Numbers: Whole numbers are known as non-negative integers and it does not include any fractional or decimal part. It is denoted as “W” and the set of whole numbers includes W = {0,1, 2, 3, 4, 5, ……….}
(iii) Integers: Integers are the set of all whole numbers but it includes a negative set of natural numbers also. “Z” represents integers and the set of integers are Z = { -3, -2, -1, 0, 1, 2, 3}
(iv) Real Numbers: All the positive and negative integers, fractional and decimal numbers without imaginary numbers are called real numbers. It is represented by the symbol “R”.
(v) Rational Numbers: Any number that can be written as a ratio of one number over another number is written as rational numbers. This means that any number that can be written in the form of p/q. The symbol “Q” represents the rational number.
(vi) Irrational Numbers: The number that cannot be expressed as the ratio of one over another is known as irrational numbers and it is represented by the symbol ”P”.
(vii) Complex Numbers: The number that can be written in the form of a+bi where “a and b” are the real number and “i” is an imaginary number is known as complex numbers “C”.
(viii) Imaginary Numbers: The imaginary numbers are the complex numbers that can be written in the form of the product of a real number and the imaginary unit “i”.
(ix) Even Numbers: The numbers which are exactly divisible by 2, are called even numbers. These can be positive or negative integers such as -42, -36, -12, 2, 4, 8 and so on.
(x) Odd Numbers: The numbers which are not exactly divisible by 2, are called odd numbers. These can be both positive and negative integers such as -3, -15, 7, 9, 17, 25 and so on.
(xi) Prime Numbers: Prime numbers are the numbers that have two factors only. (i.e.,) 1 and the number itself. In other words, the number which is divided by 1 and the number itself is called prime numbers. For example, 2, 3, 5, 7, 11, etc.
(xii) Composite Numbers: A composite number is a number that has more than two factors. For example, 4 is a composite number, as the number 4 is divisible by 1, 2, and 4. Other examples of composite numbers are 6, 8, 9, 10, and so on.
