Unit 13 L-4 Math 8
Aim:
To use rational approximations of irrational numbers to compare the size of irrational numbers, locate
them on a number line, and estimate the value of expressions (8.NS.2)
Comparing Rational and Irrational Numbers
•
__________________________ are numbers that are not rational.
•
This means they cannot be written as a ________, in the form ! , where a and b
!
are integers and b ≠ 0.
•
Square roots of integers that are ______________________ are irrational.
•
Other special numbers, like !, are also irrational.
Comparing Irrational Numbers
To compare irrational numbers that are square roots or cube roots, we can examine the
number that we are taking the square or cube root of. For example, we know that
15 < 17 because 15 is less than 17.
Exercise 1:
Fill in the blank with a < !" > sign:
a.
38 _____ 42
b.
!
!
12 _____ 21
c.
19 _____ 17
To we compare irrational and rational numbers such as 10 and 4, it is simplest to find the
decimal approximations of each irrational number and compare it to the rational number.
For example, we know that 10 ≈ 3.162. Therefore we can say that 10 < 4 because
3.162 < 4.
Exercise 2:
Fill in the blank with a < !" > sign:
a.
32 _____ 5.1
b.
!
17 _____ !
c.
!
70 _____ 4.1
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Plotting Irrational Numbers on a Number Line
• Number lines are usually marked with rational numbers. On simple number lines, we
count by integers. More complex number lines may count by ½’s or tenths. The way
the number line is divided up will depend on the numbers you are plotting on the
number line.
• No matter how the number line is set up, you will need the rational approximation of
an irrational number to graph it on the number line.
Exercise 3:
Plot the following numbers on the number line below:
Point A = 37
Point B = 42
Point C =
Exercise 4:
Plot the following numbers on the number line below:
Point D = 2
Point E = 17
Point F =
Exercise 5:
Plot the following numbers on the number line below:
Point W = 26
Point X = 88
Point Y =
77
11
24
Point G =
Point Z =
8
30
Exercise 6:
Name the point on number line associated with each number:
Point ___ =
50
Point ___ =
103
Point ___ =
90
Point ___
37
=
Point ___ =
62
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Comparing Rational and Irrational Numbers Practice
1.
Fill in the blank with a < !" > sign:
a.
50 _______ !"
!"#
b.
d.
121 _______ 125
!
e.
49 _______ 216
g.
2 _______ !
h.
5 _______ 11
2.
3.
!"
!
!"
c.
64 _______ !
!
!
!
27 _______ 2.89
!"#
f.
38 _______ !"
i.
32 _______ 10
!
Name the point on number line associated with each number:
Point ___ =
7
Point ___
=
22
Point ___ =
38
Point ___
=
15
Point ___
=
34
Place the following numbers at their approximate location on the number line below:
12,
16,
20
,
6
3. 53,
!
27
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