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**Real Numbers And Imaginary Numbers**: At a Glance

- Topics At a Glance
**Different Types of Numbers**- Natural Numbers
- Whole Numbers
- Integers and Negative Numbers
- Integers and Absolute Value
- Rational Numbers
- Irrational Numbers
**Real Numbers and Imaginary Numbers**- Different Ways to Represent Numbers
- Fractions
- Equivalent Fractions
- Mixed Numbers
- Reducing Fractions
- Comparing Fractions
- Least Common Denominator
- Addition and Subtraction of Fractions
- Multiplication of Fractions
- Equivalent Fractions and Multiplication by 1
- Multiplication by Clever Form of 1
- Multiplicative Inverses
- Division of Fractions
- Multiplication and Division with Mixed Numbers
- Decimals
- Converting Fractions into Decimals
- Converting Decimals into Fractions
- Comparing Decimals
- Adding and Subtracting Decimals
- Multiplication and Division by Powers of 10
- Multiplying Decimals
- Dividing Decimals
- Infinite Decimals
- Percents
- Portion of the Whole
- Things to Do with Real Numbers
- Addition and Subtraction of Real Numbers
- Properties of Addition
- Subtraction
- Multiplication
- Division
- Long Division Remainder
- Exponents and Powers - Whole Numbers
- Properties of Exponents
- Prime Factorization
- Order of Operations
- Even and Odd Numbers
- Infinity
- Sequences
- is Irrational
- Counting Rational Numbers
- Counting Real Numbers?
- Counting Irrational Numbers
- In the Real World
- Decimals in Use
- How to Solve a Math Problem
- I Like Abstract Things: Summary

**Real numbers** are what we get when we combine all the irrational *and* rational numbers. These numbers are "real" because they're useful for measuring things in the real world such as money, distance, temperature, and Weight Watcher points.

Absolute values and negative signs work the same way for real numbers as they do for integers. We can still use the number line to think about these concepts, but now we can take partial steps. Quick, short little shuffles of the feet, if you will.

What number times itself equals -1?

Unfortunately, there is no real number that, multiplied by itself, gives -1 nor any other negative integer. Any positive real number multiplied by itself is positive, and any negative real number multiplied by itself is also positive (link to real number multiplication). So if we want a number that creates a negative when multiplied by itself, we actually have to make up a new number - just pull one out of thin air! Whoever said there was no place for imagination in mathematics?

That's where the famous **imaginary number** *i *comes in. When you multiply *i *by itself you get -1. Now let's hop onto the back of our pet Hippogriff and fly on over to some exercises.

Number table

natural #? | whole #? | integer? | rational? | irrational? | real? | |

4 | X | X | X | X | X | |

π | X | |||||

-e | X | X | ||||

-sqrt(9) | X | X | X | |||

4/5 | X | X | ||||

sqrt(2/2) | X | X | ||||

0 | X | X | X | X |