# Math: Numbers

These lessons look at the relationship between the different types of numbers.

We all work with numbers every day, often without really thinking about them: numbers on the newspaper (prices, dates,amounts); numbers on the television or radio; sporting results; time; labels on food; money; addresses, bar codes and many more.

The following diagram shows the relationship between the types of numbers. Scroll down the page for more examples and solutions on types of numbers. ### Natural numbers

Natural numbers are positive integers. E.g. 1, 2, 3, …

### Whole numbers

Some authors take whole numbers to be 0, 1, 2, 3, …

Other authors may consider whole numbers as
… –4, –3, –2, –1, 0, 1, 2, 3, 4, …
which makes whole numbers the same as integers.

### Rational numbers

Rational numbers are numbers that can be written as a fraction where the numerator and denominator are integers. ### Irrational numbers

Irrational numbers are numbers that are not rational. In other words, they are numbers that cannot be written as fractions.

In decimal form, these numbers go on forever and the same pattern of digits are not repeated.

For example: pi(π) = 3.142.. and √2 = 1.4142…

### Real numbers

Real numbers are all the rational and irrational numbers.

Classifying Real Numbers
This video explains the different classifications of Real Numbers and has a number of examples.

The following video will describe what are natural numbers, integers, rational numbers and more.

### Squares

The square of a number is the number multiplied by itself.

For example: square of 4 = 4 2 = (4 × 4) = 16

Perfect squares are squares of whole numbers.

Some examples of perfect squares are
12 = 1, 22 = 4, 32 = 9, 42 = 16, 52 = 25, 62 = 36

### Square roots

The square root of a number n is the number that gives n when multiplied by itself.

For example: square root of 49 = 7 because (7 × 7) = 49

The square root of a perfect square would be a whole number. ### Cubes

The cube of a number is the number multiplied by itself twice

For example: cube of 4 = 4 3 = (4 × 4 × 4) = 64

Perfect cubes are cubes of whole numbers.

Some examples of cubes are 13 = 1, 23 = 8, 33 = 27, 43 = 64, 53 = 125, 63 = 216

### Cube roots

The cube root of a number n is the number that gives n when multiplied by itself twice.

For example: cube root of 27 = 3 because (3 × 3 × 3) = 27

The cube root of a perfect cube would be a whole number. Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations. 