9.2 rational and irrational numbers day 1
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Write the fraction as a decimal.
Lesson 9.2, For use with pages 475-480
1. 45
2. 59
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ANSWER 0.8
Write the fraction as a decimal.
Lesson 9.2, For use with pages 475-480
1. 45
2. 59
ANSWER 0.5
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RATIONAL and IRRATIONALNUMBERS
9.2
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Essential Questions
What is the difference between an irrational number and a rational number?
How are real numbers and the Pythagorean Theorem used in everyday life?
What types of real-life situations could the Pythagorean Theorem or square roots apply to? Why?
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Rational Numbers
Rational numbers are simply numbers that can be written as fractions or ratios
The hierarchy of real numbers looks something like this:
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1, 2, 3, 4, etc.
0, 1, 2, 3, 4, 5
.. –2, –1, 0, 1, 2, .
Rational and irrational numbers
Can be written as a fractionCan’t be written as a fraction
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Rational Numbers: Any number that can be written in fraction form is a rational number. This includes integers, terminating
decimals, and repeating decimals as well as fractions.
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An integer can be written as a fraction simply by giving it a denominator of one, so any integer is a rational number.
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A terminating decimal can be written as a fraction simply by writing it the way you say it: 3.75 = three and seventy-five hundredths =
So, any terminating decimal is a rational number.
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A repeating decimal can be written as a fraction using algebraic methods, so any repeating decimal is a rational number.
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Irrational Numbers A number that cannot be expressed as
a repeating or terminating decimal. An integer that is not a perfect square
has an irrational root.
REALS (the real numbers) The rational and irrational numbers.
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Rational Number
Fractions Ratios Whole numbers Integers Terminating
decimals (stop) Repeating decimals Square root of a
perfect square
Irrational Numbers
Non-terminating decimal
Non-repeating decimal
Square root of a number that is not a perfect square
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GUIDED PRACTICE for Example 1
Tell whether the number is rational or irrational. Explain your reasoning.
5 8
1.
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GUIDED PRACTICE for Example 1
Tell whether the number is rational or irrational. Explain your reasoning.
5 8
1.
Rational because if we write it in its decimal form then it would be 0.625 which is terminating so it is a rational number
ANSWER
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GUIDED PRACTICE for Example 1
Tell whether the number is rational or irrational. Explain your reasoning.
2. 7
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GUIDED PRACTICE for Example 1
Tell whether the number is rational or irrational. Explain your reasoning.
2.
ANSWER
Irrational because it is not a perfect square
2.64579131 . . . .
7
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GUIDED PRACTICE for Example 1
Tell whether the number is rational or irrational. Explain your reasoning.
3. 25
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GUIDED PRACTICE for Example 1
Tell whether the number is rational or irrational. Explain your reasoning.
3.
ANSWER
Rational because it is a perfect square
25
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GUIDED PRACTICE for Example 1
Tell whether the number is rational or irrational. Explain your reasoning.
4. 29
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GUIDED PRACTICE for Example 1
Tell whether the number is rational or irrational. Explain your reasoning.
4. 29
ANSWER
Rational because if we write it in its decimal from then it would be 0.2 where 2 repeating so it is a rational number
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EXAMPLE 1
Number
a. 3 4
b. 111
c. 3
Rational
Rational
Irrational
Terminating
Repeating
Non terminating and non repeating
111 = 0.0909… = 0.09
3 = 1.7320508 . . .
34 = 0.75 3
Classifying Real Numbers
Type Decimal Form Type of Decimal
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Examples Which of the following are irrational numbers?
1. 167
2. 900
3. 5476
4. 59841
1. Irrational
2. Rational -30
3. Rational 74
4. Irrational
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Homework
Page 477 #1-15 Problems 3-14 will be two points each
One point for rational or irrational One point for the reason