9.2 rational and irrational numbers day 1
DESCRIPTION
TRANSCRIPT
Write the fraction as a decimal.
Lesson 9.2, For use with pages 475-480
1. 45
2. 59
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
RATIONAL and IRRATIONALNUMBERS
9.2
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?
Rational Numbers
Rational numbers are simply numbers that can be written as fractions or ratios
The hierarchy of real numbers looks something like this:
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
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.
An integer can be written as a fraction simply by giving it a denominator of one, so any integer is a rational number.
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.
A repeating decimal can be written as a fraction using algebraic methods, so any repeating decimal is a rational number.
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.
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
GUIDED PRACTICE for Example 1
Tell whether the number is rational or irrational. Explain your reasoning.
5 8
1.
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
GUIDED PRACTICE for Example 1
Tell whether the number is rational or irrational. Explain your reasoning.
2. 7
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
GUIDED PRACTICE for Example 1
Tell whether the number is rational or irrational. Explain your reasoning.
3. 25
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
GUIDED PRACTICE for Example 1
Tell whether the number is rational or irrational. Explain your reasoning.
4. 29
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
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
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
Homework
Page 477 #1-15 Problems 3-14 will be two points each
One point for rational or irrational One point for the reason