Types of Numbers in Math with Examples Properties & Definitions

The use of numbers in math can be confusing to students. There are many types of numbers and some people may not know the difference between them. Here is a list of different types: natural, whole, integer, rational, irrational. The article also goes on to describe how each type is used in math and what they look like when written out as an equation or graphically on a number line.

Types of Numbers

In math, there are two types of numbers: whole numbers and fractions. Whole numbers include 0-9 and fractions include anything with a decimal point such as 3/4 or .75. There is also another type of number called an irrational number which includes pi (3.14) and the square root of 2 (.5).

Types of Numbers in Mathematics List

  • Rational Number
  • Irrational Number
  • Real Number
  • Integer
  • Natural Number
  • Fraction
  • Complex Number
  • Number
  • Decimal
  • Composite Number
  • Prime Number
  • Square Number
  • Triangular Number
  • Negative Number

Rational Number

A rational number is a number that can be expressed as the quotient or fraction of two integers, a numerator,Rational Number and a denominator. Rational numbers are part of the set of real numbers and their decimal representations continue indefinitely without repeating digits. The decimal representation for an irrational number will eventually form a pattern that repeats itself endlessly.

In mathematics, rational numbers are often represented using fractions with integer coefficients rather than decimal ones, but they may also be written in any other form if it makes them easier to read or understand.

For example, 1/2 = 0.5 would represent one-half to one decimal place accuracy while 2/3 = 0.666…would represent two-thirds to three decimal places accuracy because both have terminating decimals.

Try Also: Types of Angles

Irrational Number

Irrational numbers are funny things. They can’t be written as fractions, like rational numbers (a/b). Irrational numbers have decimals that go on forever without repeating themselves. The most famous irrational number is Pi, which has a decimal of 3.141592653…

Irrational Number

Try Also: Difference Between Parabola And Hyperbola

Real Number

A real number is a number that can be calculated without the use of an imaginary number. They’re also known as rational numbers and are a subset of all real numbers. Examples include 1, 2, 3, 4, 5… etc. All other values such as pi (3.14) or π (3.14159…) are not considered to be real numbers because they cannot be expressed on the standard ruler scale with integers only (1-9).

Real Number

Try Also: Types of Triangles


An integer is a whole number with no fractional part. It can be positive, negative, or zero. There are many different types of integers such as natural numbers, rational numbers, and irrational numbers just to name a few.


Try Also: 17 Branches of Mathematics

Natural Number

Natural numbers are a subset of the set of integers. They are typically used in counting, but also have many other uses in mathematics. For example, natural numbers can be used to construct patterns that recur across many different scales.

Natural Number

The Fibonacci sequence is one such pattern; it describes how adding two successive terms leads to the next term as follows: 1, 1, 2, 3, 5, 8… These series represent proportions found throughout nature and art forms like paintings or music compositions.

Natural number’s properties make them ideal for use in modeling systems with similar properties like population growth or chemical reactions; they’re an important part of most mathematical fields including calculus and linear algebra.


A fraction refers to an expression that shows division where both quantities are not integers (whole numbers) but rather fractions (numbers with a line over them). For example 2/3 = 2 divided by 3 or 1/4 = 4 divided by 4. This means that you divide one quantity by another resulting in a ratio such as 1:2 for every time you multiply two items together there will be three.



Complex Number

A complex number has both imaginary and real parts that are multiplied together. The real part can be expressed as x+iy; where x is called the real component and y is called the imaginary component.

This means that if you were given two different values for x or y, they would make up two different representations of a single complex number because one would have an imaginary part (y) while another would have a real (x).”


Numbers are useful because they allow us to measure things. For example, if you have two apples and an orange, but only one bag of chips, the number of apples equals 2 while the number of oranges equals 1.


A decimal is used to show numbers with fractions. Mathematics uses it as a way of representing an exact number without having to use the whole number system. For example, if I have 1/2 of my cookie left, I can represent this by saying “0.5” which means that there are 2 digits after the decimal point and they are both zeros because I would have 5 cookies total.

Decimals are important in math because they allow us to express very small or very large numbers that cannot be expressed using all-natural numbers available for counting on our hands or fingers!

Composite Number

Composite numbers are the biggest group of whole numbers, according to mathematicians. They are formed by adding together two or more prime numbers. The number 10 is a composite number because it is made up of 2 and 8, which are both prime numbers. Composite Numbers have many interesting properties that differentiate them from other groups of whole numbers.

Prime Number

In mathematics, a prime number is a natural number that has exactly two distinct natural numbers as its only factors. A prime number can be written as 2∙2 and 3∙3 and 5∙5 etc. The first few prime numbers are 2, 3, 4, 5, 7, and 11.

Prime numbers are important in mathematics because they’re the building blocks of all other whole numbers. They’re also very useful for solving math problems involving addition or multiplication with large integers (numbers without decimal points).

For example: if you want to find out what 9+14 equals then you would use this formula: 9+14=23 which means 23 is the answer! And vice versa if you wanted to know what 23-

Square Number

A Square Number is a number that has an odd number of digits and ends with the digit “4” or “9”. The word “square” in mathematics refers to something that can be multiplied by itself. You can find out if a number is a square using the formula: (number)2= (answer). For example, 25² = 625.

Triangular Number

A triangular number is a number that can be created by multiplying three consecutive numbers together. The first triangular number, for example, is 1x2x3=6. Triangular numbers are simple to calculate and have many applications in mathematics. They are also fun to use as the answer to math problems.

Triangular Numbers can help you solve all kinds of math problems. You may not realize it but they are actually used every day so if you know how to use them then there’s no limit on what you could do with them!

Negative Number

Many people think that a negative number is the opposite of a positive number. For instance, if you have two apples and eat one apple then you would be left with one apple. If someone told you that they had -2 apples, it would mean that they only had 2 apples (and not 8).

This means that their total amount of apples was less than zero. Negative numbers are used in mathematics to show what’s leftover after the addition or subtraction of other numbers;

for example, when we subtract 3 from 5 we get 2 because there are now two more things leftover than before (3-5=2). The place value system makes this easier to understand by using digits like 1023-35 which will have different values. Types of Numbers.

Discrete and continuous numbers

Discrete numbers represent an exact value without any gaps or spaces in-between the digits while continuous numbers have infinite values so there’s no clear cut-off point where their magnitude ends. This means that once you get up into larger magnitudes such as 10^99, then it would be considered a continuous number since you cannot know for sure when its magnitude ends just by looking at it.

Constructing numbers

there are different Types of Numbers in Math but Constructing numbers is a complicated process that requires knowledge of the number system and principles. The first step to constructing numbers is understanding how to count, starting with one and continuing until we reach “ten.” After counting to ten, we need to understand how many times we counted by two’s.

For example: If you counted up from 1-10 once or twice then your answer would be 11 (1+2=3×2). When working through this problem on paper, make sure you write down what you are doing as it will help prevent mistakes later on.

Once the student has determined their answer they should subtract six from that number because there are six steps between each set of 10 digits (e.g., the difference between 40.

FAQs (Frequently Asked Questions)

Q. What are the five types of numbers?

Ans: In mathematics, there are five types of numbers: whole numbers, natural numbers, integers, rational numbers, and irrational numbers. Whole Numbers consist of any number that is not a fraction or decimal. Natural Numbers include all whole numbers and zero. Integers can be positive or negative and represent all the real-life counting we do in our lives. Rational Numbers are fractions that contain an integer on top and bottom while Irrational Numbers cannot be expressed as a ratio between two integers such as pi (3.14).

Q. How Many Types of Numbers?

Ans: There are many types of numbers in mathematics. These include integers, rationals, irrationals, and real numbers. some of them can be found on a graph or line on a coordinate plane (rationals), which is an ordered pair (x,y) where x represents the distance traveled eastward from the origin; y represents the distance traveled northward from the origin; both measured in units called “meters” or “pixels”; coordinates represent points with respect to an axis system.

Q. How do you classify numbers?

Ans: Mathematics is a vast and complex subject that has many branches. One of the most fundamental concepts in mathematics is classification, which refers to how we identify and organize different types of numbers. For example, integers are whole numbers without any decimals or fractions; rationals are numbers that can be expressed as a ratio such as ½, ⅓, ¼; irrationals are real numbers that do not have any repeating pattern like π or √2.

Related Articles

Leave a Reply

Your email address will not be published.

Back to top button