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**(as opposed to fake numbers?)**

REAL NUMBERS (as opposed to fake numbers?)

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**Two Kinds of Real Numbers**

Rational Numbers Irrational Numbers

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**Branching Real Numbers**

Rational Irrational Now let’s break these subsets down further!

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**Rational Numbers A rational number…**

is a real number that can be written as a ratio (fraction) of two integers. written in decimal form is terminating (ends) or repeating (same pattern of numbers).

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**Examples of Rational Numbers**

16 1/2 3.56 -8 1.3333… - 3/4 Can you write 16 as a ratio? Now try writing -8 as a ratio!

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**Irrational Numbers An irrational number**

is a number that cannot be written as a ratio (fraction) of two integers. written as decimals are non-terminating (never end!) and non-repeating (no pattern).

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**Examples of Irrational Numbers**

Square roots of non-perfect “squares” Pi 17 What is the square root of 17? What is another non-perfect square?

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**Integers One of the subsets of rational numbers**

So what do integers branch off of?

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Integers Integers are rational numbers because they can be written as fraction with 1 as the denominator. *Remember* Rational numbers can be written as a ratio (or in other words, a fraction)

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**What are integers? Integers are the whole numbers and their opposites.**

Examples of integers are 6 -12 186 -934 What do you notice about these integers?

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**Whole Numbers One of the subsets of rational numbers and integers**

So what do whole numbers branch off of?

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Whole Numbers All positive numbers that are counting numbers plus zero. How can you remember that zero goes with whole numbers? Examples: 0, 1, 2, 3, 4, 5 …

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Natural Numbers One of the subsets of rational numbers, integers and whole numbers So what do natural numbers branch off of?

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**Natural Numbers All of your counting numbers**

What numbers do you count with?

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**Classify the following Numbers**

What subset(s) do the following numbers belong to? Remember they could belong to more than one! Whole, Integers, Rational, and Real

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**Classify the following Numbers (Con’t)**

4 Natural, Whole, Integer, Rational, Real -9 Integer, Rational, Real Π Irrational, Real

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**Classify the following Numbers (Con’t)**

3/4 or 0.75 Rational and Real 4 Natural, Whole, Integer, Rational, Real 15 Irrational, Real

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