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REAL NUMBERS

(as opposed to fake numbers?)

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Natural Numbers• Are the set of

counting numbers.

• Example:{1, 2, 3,…}

Zero is not a natural number

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Whole Numbers:

Whole numbers are the same as the natural number. The only difference is that whole numbers include the number zero.

All Natural Numbers are Whole Numbers.

W

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Integers

• Include all positive whole numbers, negative whole numbers and zero

• Example {…,-3, -2, -1, 0, 1, 2, 3,…}

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All Natural Numbers are Integers.

• Natural numbers is subset of the Whole Numbers.

• Whole Numbers is subset of Integers.

Natural Number is subset of Integers

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Examples of Integers

6-120186-934

Integers

Whole Numbers Natural

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Rational Numbers

• Can be written as a ratio of two integers.

• e.g.:

• Can be written in decimal form is terminating or repeating.

b

a

9

4

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Terminating Decimal:

Are decimals that contain a finite number of digits.• Examples:

36.8 = 368/100.125= 125/10004.5= 45/10

Terminating Decimals are Rational Numbers because they can be written as fractions

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Repeating Decimal:

Are decimals that contain an infinite number of digits.Examples: 0.333… , 7.689689…

Repeating Decimals are Rational Numbers because they can be written as fractions

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Examples of Rational Numbers

• 16• 1/2• 3.56

• -8• 1.3333…• - 3/4

Rational Numbers

Integers Whole Numbers Natural

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All Natural Numbers and All Integers are Rational Numbers• Natural numbers is one subset of the Rational Numbers.

• Integers are another subset of Rational Numbers.

• Whole Numbers is another subset of Rational Numbers.

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All Natural Numbers and All Integers are Rational NumbersNatural numbers, whole numbers and integers are Rational numbers because you can write them as a fraction

1

189189

1

33

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Irrational Numbers• Irrational numbers are any numbers that

cannot be expressed as fractions (ratio of two integers) .

• They are expressed as non-terminating, non-repeating decimals; decimals that go on forever without repeating a pattern.

• Examples of irrational numbers:• 0.34334333433334…• 45.86745893…• (pi) = 3.14…•

I

2

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Real Numbers

Irrational Numbers

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Rational Numbers

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SummaryReal Numbers

Rational Numbers

Integers

Whole Numbers

Natural

Irrational Numbers