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Classifying and Identifying Real Numbers

(as opposed to fake numbers?)

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ObjectiveIdentify and classify rational and irrational numbers

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THINK SHARE

How many numbers are between 0 and 1 on the number

line?

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Real Numbers

Real Numbers are every number.

Therefore, any number that you can find on the number line.

Real Numbers have two categories.

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Two Kinds of Real Numbers

• Rational Numbers

• Irrational Numbers

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Rational Numbers

• A rational number is a real number that can be written as a ratio (fraction) of two integers.

• A rational number can be written as an integer, terminating or repeating decimal.

Examples of Rational Numbers

•16•1/2

•-8•1.3333…

•- 3/4

Integers

One of the subsets of rational numbers

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Integers

• Consist of the natural numbers, their opposites and zero

-4, -3, -2, -1, 0, 1, 2, 3, 4

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Integers

• Integers are rational numbers because they can be written as fraction with 1 as the denominator.

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Types of Integers

• Natural Numbers(N): Natural Numbers are counting numbers from 1,2,3,4,5,................

• Whole Numbers (W): Whole numbers are natural numbers (counting numbers and zero. 0,1,2,3,4,5,...............

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1212

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Irrational Numbers

• An irrational number is a number that cannot be written as a ratio (fraction) of integers.

• In decimal form, they are the numbers that are non-terminating and non-repeating.

Examples of Irrational Numbers

• Square roots of non-perfect “squares”

• Pi 3.1415……

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2.2360

Try this!Thumbs up- rational

Thumbs down- irrational• a) Irrational

• b) Irrational

• c) Rational

• d) Rational

• e) Irrational66 e)

d)

25 c)

12 b)

2 a)

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Quick Question???

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Classifying Real Numbers

Write all classifications that apply to each number.

5 is a whole number that is not a perfect square.

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irrational, real

–12.75 is a terminating decimal.–12.75rational, real

16 2

whole, integer, rational, real

= = 24 2

16 2

I DO.

WE Do.

You Do

State if each number is rational, irrational, or not a real number.

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irrational

0 3

rational

0 3

= 0

Exit Ticket

A.

B.

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Steps for Comparing

• One type of problem strategy is to use a visual.

• Today’s visual is the number line.

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Model

• Change the numbers to a decimal.

• Is the number greater than zero?• What two whole numbers is the

number between?• Is it closer to a quarter? a half?

three-quarters?

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WE DO-PracticeRally Coach

• Partner A asks the questions and Partner B responds by answering and placing the number on the number line.

• Partner B asks the questions and Partner A responds by answering and placing the number on the number line.

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I Do

• Place the following numbers on the number line.

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Thinking for Tomorrow

• Where do you think the following numbers would fall on the number line?

•√15 √5 √9

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