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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.
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Examples of Rational Numbers
•16•1/2
•-8•1.3333…
•- 3/4
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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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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.
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Examples of Irrational Numbers
• Square roots of non-perfect “squares”
• Pi 3.1415……
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2.2360
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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.
5
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
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State if each number is rational, irrational, or not a real number.
21
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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