1-3 Exploring Real Numbers

Let’s start on the inside…what are natural numbers?

Natural numbers are the counting numbers…1, 2, 3, 4 …

1, 2, 3, 4…

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Next come the whole numbers

Whole numbers are zero and the natural numbers.

1, 2, 3, 4…

0, 1, 2, 3…

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Integers

Integers are whole numbers and their opposites.

1, 2, 3, 4…

0, 1, 2, 3…

-2, -1, 0, 1, 2…

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Rational numbers can be written in the form and

Includes all repeating and terminating decimals

1, 2, 3, 4…

0, 1, 2, 3…

-2, -1, 0, 1, 2…

b

a0b

9

4,25.0,3.0,

3

1,2

11

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Irrational numbers cannot be written in the form

Includes all non-repeating and non-terminating decimals.

1, 2, 3, 4…

0, 1, 2, 3…

-2, -1, 0, 1, 2…

b

a

9

4,25.0,3.0,

3

1,2

11

2

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bers

Real numbers are all the numbers on the continuous number line with no gaps. Real numbers may be rational or irrational.

1, 2, 3, 4…

0, 1, 2, 3…

-2, -1, 0, 1, 2…9

4,25.0,3.0,

3

1,2

11

2

π Clas

sify

ing

Num

bers

Real numbers are all the numbers on the continuous number line with no gaps. Real numbers may be rational or irrational.

1, 2, 3, 4…

0, 1, 2, 3…

-2, -1, 0, 1, 2…9

4,25.0,3.0,

3

1,2

11

2

π Clas

sify

ing

Num

bers

So what other type of number can there be?

Real numbers are all the numbers on the continuous number line with no gaps. Real numbers may be rational or irrational.

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bers

So what other type of number can there be?

Imaginary numbers

Imaginary numbers can be fun!

Com

parin

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rsInequality

There are 5 types:

>

<

greater than

greater than or equal to

less than

less than or equal to

not equal to

Absolute Value is a distanceIt tells how far a number is from zero

A distance can NEVER be negative

Opposites – “live” on opposite sides of zero. Zero doesn’t have an opposite.