LESSON 9.2 - Rational and Irrational Numbers
Goal: Work with irrational numbers.
Warm-Up:
Convert the following fractions into decimals without a calculator:
1.
2.
3. Describe how you would show that a decimal repeats.
Vocabulary
Real Numbers:
Examples: ______________________________________________________________________
Imaginary Numbers:
Examples: _____________________________________________________________________
Rational Numbers:
Examples: ___________________________________________________________
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Irrational Numbers:
Examples: ___________________________________________________________
Integers:
Examples: ______________________________________________________________________
Whole Numbers:
Examples: _____________________________________________________________________
Natural Numbers:
Examples: ___________________________________________________________
EXAMPLE 1 - Classifying Real Numbers as Rational or Irrational
Number
a)
b)
Decimal
Type of Decimal (repeating, terminating or Rational or
non-terminating)
Irrational
4
5
7
22
2
c)
Notice that if n is a
positive integer and
is not a perfect
square, then n and
 n are
irrational numbers.
2
Now You Try It! Tell whether the number is rational or irrational. Explain your reasoning.
9
1)
20
2)
13
3)
5
6
4)
81
EXAMPLE 2 - Comparing Real Numbers
Graph the pair of numbers on a number line. Then copy and complete the statement with <
or >.
a) 3 _____ 3
MAKE A PREDICTION>>>>>>
2
2
b)
_____
3
3
Use a calculator to approximate the square root and write any fractions as decimals. Then graph the
numbers on a number line and compare.

a)
1.5 1.75

2
2.25 2.5
2.75

b)
0
3
So, 3 ______ 3
3.25

So,
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
2
2
_____
3
3
WATCH OUT
You may need to use
parenthesis when
using a calculator to
approximate a square
root.
Now You Try It! Graph the pair of numbers on a number line.
Then complete the statement with <, >, or =.
5)
6 _____ 3
2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4
3
6)
49 _____ 7
6
7)
6.5
7
7.5
8
1
1
_____
9
9
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
EXAMPLE 3 - Ordering Decimals
Put the following decimals in order from least to greatest:
0.63
0.63
0.633
0.636
1. Write each decimal out to at least one place beyond the longest decimal. Since you have three
numbers repeating in the last decimal, write them out to six places so you can at least get one
“repeat”.
0.63
=
0.63
=
0.633 =
Notice that the first
two digits after the
decimal point are
the sane for each
number. Use the
second pair of
digits to order the
decimals.
0.636 =
2. Now write them in order from least to greatest:
EXAMPLE 4 – Writing Rational and Irrational Numbers
Write a rational number and an irrational number between 5 and 6.
Now You Try It!
Write a rational number and an irrational number between 6 and 7.
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