Number Systems

Number Systems

Number: Arithmetical value representing a particular quantity. The various types of numbers are Natural Numbers, Whole Numbers, Integers, Rational Numbers, Irrational Numbers, Real Numbers etc.

Natural Numbers

Natural numbers(N) are positive numbers i.e. 1, 2, 3 ..and so on.

Whole Numbers

Whole numbers (W) are 0, 1, 2,..and so on. Whole numbers are all Natural Numbers including ‘0’. Whole numbers do not include any fractions, negative numbers, or decimals.

Integers

Integers are the numbers that include whole numbers along with negative numbers.

Rational Numbers

A number ‘r’ is called a rational number if it can be written in the form p/q, where p and q are integers and q ≠ 0.

Irrational Numbers

Any number that cannot be expressed in the form of p/q, where p and q are integers and q≠0, is an irrational number. Examples: √2, 1.010024563…, e, π

Real Numbers

Any number which can be represented on the number line is a Real Number(R). It includes both rational and irrational numbers. Every point on the number line represents a unique real number.

Imaginary Numbers

Imaginary numbers are those numbers which we can just imagine but cannot physically perceive.

For Example √-1, √-3, etc, √-1 is represented by i, Square Root of all imaginary number is imaginary.

Complex Number

The combination of Real and Imaginary numbers is called complex numbers. Example: (2+5i) , (1+3i) etc.

Even number

An integer that is “evenly divisible” by two. Example 2,4,8,….. etc.

Odd number

All the Natural numbers which are not Even numbers. Example 1, 3, 19, 21,….. etc.

Prime number

An integer is greater than 1 which is only divisible by 1 and the number itself are called prime numbers. Example 2,3,5,7,11,13,….etc

Co-Prime Number

If the only positive integer (factor) that divides both of them is 1. Examples:- 13 and 14 are co-prime, being commonly divisible only by 1, while 22 and 24 are not co-prime because they are both divisible by 2.

Composite Number

All the natural numbers greater than 1 which are divisible by at least one more number other than 1 and the number itself are called composite numbers. Example: 6 can be divided exactly by 3 or 2 (as well as 1 and 6), so 6 is a composite number. But 7 cannot be divided exactly (except by 1 and 7), so is NOT a composite number (it is a prime number).

Place value

The place or position of a digit in a number is called its place value. Example: Place value of 2 in 4289 is 200.

Face value

The real value of any digit in a certain number is called its face value.

For example, the face value of 2 in 7246 is 2.