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Rational and Irrational Numbers Examples,
Different Number Types in Math

Numbers in Math can be classed into specific groups of numbers.
If you want to go about grouping numbers according to their specific type, it’s important to be familiar with the main different number groups that exist.

Below are common groups that different numbers can be categorized as.

Different Number Types in Math:

Natural Numbers

The natural numbers in Math are often referred to as ‘counting numbers’. They are whole numbers that are larger than zero, the numbers that you probably use every day to count things with.

{ 0 , 1 , 2 , 3 , 4 , …… }


With groups of numbers, integers are whole numbers that can be of both positive and negative value, but also including zero.

{ …… , -3 , -2 , -1 , 0 , 1 , 2 , 3 , ……}

Rational and Irrational Numbers Examples


Rational numbers in Math are numbers that can be written as a fraction or quotient of two integers.

For example  \bf{\frac{1}{2}} , \bf{\frac{3}{4}}  ,  and also are rational.

A whole number like  4  is also a rational number in groups of numbers,

as it can be written as the fraction  \bf{\frac{4}{1}}.


Unlike rational numbers, irrational numbers are numbers that can’t be written as a fraction or quotient of two integers.

Classic examples of irrational numbers are   π  and  √2 .

Real Numbers

Each of the number types in the previous groups are real numbers, including irrational numbers.

Many numbers in Math fall into different groups of numbers.

Prime Numbers

A prime number will be any whole number greater than 1 which can only be divided evenly by itself and 1.

The numbers   3 , 11  and  17  are prime numbers, but there are many more that exist.

Groups of Numbers, Infinity

A specific case that should also be included in a groups of numbers section is ‘Infinity’.

Now infinity isn’t actually a number, it is really an idea, a suggestion.
The idea that an amount of something is unlimited, going on and on with no ending.

The symbol for infinity is  \infty.

The group of all Real Numbers in Math are an example of an infinite group.

Because you can write something like   4’000’000………,

and keep writing zeroes on and on forever with no end.

Many fractions also have a decimal form that is infinite.
\bf{\frac{1}{9}}   produces a decimal form that is infinite.

\bf{\frac{1}{9}}  =  0.1111…….,  the one’s go on forever.

It’s the case that infinity does go in both directions, we also have negative infinity,  {\text{-}}\infty.

Where numbers can go on and on without end in a negative direction.   -1 , -2 , -3 , …..

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