# Types of Numbers in Mathematics

A number is a way of expressing or representing the value or count of a given set, using digits or other symbols which gives consistent result on every count of the same sets. The same sequence of symbols or numbers may represent different types of numbers in different numeral systems.

The number which represents the result of any calculation is called its value. Ideally, types of number in the number system will have the following characteristics:

1. Represent a useful set of numbers.
2. Every number represents a unique and standard representation.
3. Reflect on the algebraic and arithmetic structure of the numbers.

Representation of numbers has been classified to include Zero, Negative Numbers, Rational Numbers, Real Numbers, and Complex Numbers.

## Main Classification or Types of Numbers

Below are the main types of numbers, knowing these will help us in identifying the numbers.

### Natural Number

Natural Numbers are sometimes called Whole Numbers or Counting Numbers, which are represented by N in the collective set. Natural Numbers are one of the most basic types of numbers. The arithmetic operation of addition (+) and multiplication (x) of two natural numbers will result in Natural Number. The whole number starts at 0 in addition to the Natural Number System.

Natural Number: {1, 2, 3, 4, 5, 6, 7, 8, 9, …}

### Integer

The integer is an extension of Natural numbers along with Zero and their Negative Numbers. The set of Integer is represented by Z in the collective set. In other words, the natural numbers form a subset of the Integers. The arithmetic operation of any two integers will result in an integer. However, decimals are not considered an integer.

The natural numbers without zero are called positive integers. The natural numbers less than zero are called negative integers.

Z comes from the German word “Zahlen”, which means “to count”.

Integers: {…, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, …}

### Rational Number

A Rational number is a number that can be noted as a division with a whole number numerator and a positive number denominator. composed as two whole numbers, the numerator, and the denominator, with a separating bar between them. The fraction m/n represents m parts of an entire separated into n equivalent parts.

Fractions can be more prominent than, not exactly, or equivalent to 1 and can likewise be certain, negative, or zero. The short form for the rational numbers is Q. Q comes from the word ‘quotient’.

Rational Number: 1/2 or 0.5

### Irrational Number

An irrational number is a number that can’t be composed of rational numbers. In decimal structure, it never closures or rehashes the arrangement. Not all numbers are levelheaded, there are conditions that can’t be unraveled utilizing portions of whole numbers.

Irrational numbers example is the square root of 2 and the Value of Pi.

### Real Number

Real numbers are the arrangement of numbers containing the entire set of rational numbers and the entire set of irrational numbers. The real numbers are “all the numbers” on the number line.

There are limitlessly numerous real numbers similarly as there are vastly numerous numbers in every one of different arrangements of numbers.

### Complex Number

Moving one level up in number systems, Complex numbers is the sum of a real number and imaginary real numbers. Complex numbers are represented as: a + ib. Where i represent an imaginary part.

The real numbers, in the complex number system, are written in the form a + i0 = a; where the value of ‘b’ is zero. Hence, ‘a’ is a real number.

## Other Classification or Types of Numbers

Apart from the above types of numbers, there are many other types of numbers, out of which a few important types are given below.

### Even Odd Number

A number is said to be an Odd Number when that number is not divisible by 2 and a number is said to be an Even Number when the number is divisible by 2. For Example: 4 is an Even Number and 5 is an Odd Number.

### Prime Number

Prime numbers are the positive integers that have only two factors, 1 and the integer itself. It means that any number that is divisible by itself is called a Prime number. Let’s take an example of the number 3, it can be factored as 3 and 1. So, 3 is a Prime number.

### Composite Number

Numbers other than Prime numbers are known as Composite numbers. In other words, a Composite Number is a number that has factors other than 1 and the number itself. For example: 4, 6, etc…

### Perfect Number

A number is called to be a Perfect number if that number is a Positive number and is equal to the sum of all divisors other than the number itself. For Example: 6 has divisors 1, 2 and 3 (excluding itself), and sum of all divisors 1 + 2 + 3 = 6, so 6 is a perfect number.

### Fibonacci Number

Fibonacci Numbers are denoted as the Fibonacci Series, which starts with 0 and 1 beyond this each number is the sum of the two preceding ones. For Example: 0, 1, 1, 2, 3, 5, 8, 13, … etc.

## Practice Questions

Below are a few practice questions on types of numbers:

### True or False

1. Every whole number is a natural number?
2. Every natural number is a whole number?
3. Every integer is a whole number?
4. Every integer is a rational number?
5. Every rational number is an integer?
6. Every rational number is a whole number?
7. Every irrational number is a real number?
8. Every real number is an irrational number?
9. The sum or difference between a rational number and an irrational number is irrational?
10. The product or quotient of a non-zero rational number with an irrational number is irrational?

### Solution

1. False, because zero is a whole number but not a natural number.
2. True, because every integer Z can be expressed in the form Z/1, and so it is a rational number.
3. False
4. True, since the collection of whole numbers contains all the natural numbers.
5. False, – 10 is not a whole number.
6. False, 1/3 is a rational number but not a whole number.
7. True, since the collection of real numbers is made up of rational and irrational numbers.
8. False, 2 is real but not irrational.
9. True
10. True

## Final Words on Types of numbers

It’s very basic and essential to know different types of numbers, and how to identify and use this classification in solving problems. There may not be any direct questions on the types of numbers, but one should have clear concepts.