# Classification of numbers

The chart below will help you with the classification of numbers a lot. It will makes things crystal clear.

Important observations you need to make from the chart. Observation #1:

Notice that √(9) is a natural number. It is because √(9) = 3

Observation #2:

Notice that the only difference between natural numbers and whole numbers is the zero.

Whole numbers = Natural numbers + zero

Observation #3:

Notice that the difference between whole numbers and integers are the negative numbers.

Integers = Whole numbers + the negative of the whole numbers

Observation #4:

All integers are fractions. Not all fractions are integers

Example: -2 is an integer and can be written as -2/1 to make it a fraction.

However, -1/3 = -0.333333333 is not an integer

Observation #5:

Fractions can be written as a terminating decimal or a repeating decimal

Example: 1/2 = 0.5 and 0.5 is a terminating decimal. 1/3 = 0.3333333 and 0.3333333 is a repeating decimal

Observation #6:

Rational numbers = Integers + fractions

Observation #7:

Irrational numbers are numbers that cannot be written as a fraction

Example: pi= 3.14..., 2.224879566117426874, √(7)

Another way to see them is that they are neither repeating decimals nor terminating decimals

Observation #8:

Real numbers = rational numbers + irrational numbers

Observation #9:

The difference between complex numbers and real numbers is that complex numbers give solutions for the following expressions and more!

√(-7), √(1-8), √(-25) = 5i, etc...

Among the different types of numbers, fractions is among the toughest to understand

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