# Real Numbers

### Real Numbers are just numbers like:

1 | 12.38 | −0.8625 | \frac{3}{4} | π (pi) |
198 |

In fact:

Nearly any number you can think of is a Real Number

### Real Numbers include:

Whole Numbers (like 0, 1, 2, 3, 4, etc) | ||

Rational Numbers (like 3/4, 0.125, 0.333..., 1.1, etc ) | ||

Irrational Numbers (like π, √2, etc ) |

Real Numbers can also be **positive**, **negative** or zero.

### So ... what is NOT a Real Number?

Imaginary Numbers like √−1 (the square root of minus 1)are not Real Numbers |
||

Infinity is not a Real Number |

Mathematicians also play with some special numbers that aren't Real Numbers.

## The Real Number Line

The Real Number Line is like a geometric line.

A point is chosen on the line to be the **"origin"**. Points to the right are positive, and points to the left are negative.

A distance is chosen to be "1", then whole numbers are marked off: {1,2,3,...}, and also in the negative direction: {...,−3,−2,−1}

**Any point on the line is a Real Number:**

- The numbers could be whole (like 7)
- or rational (like 20/9)
- or irrational (like π)

But we won't find Infinity, or an Imaginary Number.

## Any Number of Digits

A Real Number can have any number of digits either side of the decimal point

- 120.
- 0.12345
- 12.5509
- 0.000 000 0001

There can be an infinite number of digits, such as \frac{1}{3} = 0.333...

## Why are they called "Real" Numbers?

**Because they are not Imaginary Numbers**

The Real Numbers had no name before Imaginary Numbers were thought of. They got called "Real" because they were not Imaginary. That is the actual answer!

## Real does not mean they are in the real world

They are **not** called "Real" because they show the value of something **real**.

In mathematics we like our numbers pure, when we write 0.5 we mean **exactly** half.

But in the real world half may not be *exact* (try cutting an apple **exactly** in half).