4
: Irrational Numbers
A rational number is an ___________________________ value. It is a number that can be written as a
_______________________. It has a _______________________ or ____________________ decimal.
An irrational number is an __________________________ value. It is a number that CANNOT be written as a fraction. It has a never ending, never repeating decimal.
What does a decimal number that terminates look like?
What does a decimal number that repeats look like?
Steps to determine if a number is irrational or rational:
1) Use your calculator to find the value (approximate or exact) of the number.
2) Determine if it is a repeating or terminating decimal (rational) or not (irrational).
Example 1: Classifying Numbers
Tell whether each number is rational or irrational. Explain how you know!
a) [pic] b) [pic] c) [pic]
d) [pic] e) 3 f) 0
Why can’t an irrational number have a 0 in the denominator?
Number Types
[pic]
Together, the rational and irrational numbers form the set of real numbers!
Steps to order numbers:
1) First put the numbers all in decimal form.
2) Order the numbers (remember to think about negatives!)
Example 2: Ordering Irrational Numbers on a Number Line
Use a number line to order these numbers from least to greatest. Also decide if they are rational or irrational (use R and I), exact or approximate (use E and A).
Homework: Pg. 211 #3, 4, 5, 7, 8, 10, 11, 12, 14, 15
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