2.1 The Real Number Line
Learning Target: __________________________________________________________________
Real numbers: The set of ____________ and _____________ numbers;
every real number is either ________, ________, or _____.
Points to the left of zero represent __________ numbers;
Points to the right of zero represent __________ numbers;
Zero is neither positive nor negative
Rational numbers
Any number that can be expressed as a _______________:
Natural (Counting) numbers: ____________________
Whole numbers: ______________________________
Irrational Numbers
Any number that cannot be expressed as a
______________:
;
25  5i
Fractions/mixed numbers: _________________________
Decimals: ___________________________________
Integers: ____________________________________
THE REAL NUMBER LINE
COMPARE INTEGERS

a number to the RIGHT on a # line is _________ _____ ( ) a # to its left

a number to the LEFT on a # line is _________ _____ ( ) a # to its right

A NEGATIVE number will ALWAYS be _________ _____ ( ) a positive number

A POSITIVE number will ALWAYS be _________ _____ ( ) a negative number
Examples
1) Graph -4 and 1 on a number line and write 2 inequalities that compare -4 and 1:
_________________
_________________
2) Graph 5 and -2 on a number line and write 2 inequalities comparing them: ___________________
___________________
Practice

Compare: -5, ____5; 2_____-3; -2 ___ -4,
-3 ___ 2;
-5 ____ -6;
-1 _____ 1
Graph, Compare, and Order Real numbers
3) Graph -0.8 and 4 on a number line and write 2 inequalities comparing them: ___________________
7
___________________
Because the numbers you are comparing are not integers, use a number line that has scale marks in
smaller units.
When you work with fractions, it is usually easier to convert the fraction into a decimal (use calculator)
1
3
4) Write the following numbers in increasing order: 
2, 4, 0,1.5, ,  

2
2
a. First change all fractions into decimals:___________________________________________________
b. Next, group negative numbers at the beginning, positives numbers at the end:
_____________________________________________________________________________
c. Then, graph the numbers on a number line (you may skip this step)
d. Finally, list the numbers from least to greatest (left to right) ___________________________________
TRY IT! Write the numbers in increasing order:
1

6) 
3, 3, 3.2,  , 8, 4.5
5 3

5) 
3, 0, 4,  , , 1

4 2


___________________________________

2
___________________________________
Real life example:
The Table below shows the low temperatures in Nome, Alaska for five days in February:
Date
Low
Temperature
Feb. 22
Feb. 23
Feb. 24
Feb 25
Feb 26
-20oF
-11oF
20oF
17oF
-15oF
7) Order the temperatures from low to high. ______________________________________________________
8) Which dates had low temperatures above 10oF? ____________________________________________
8) Which date had the lowest low temperature? ______________ What was the temperature? ___________
9) Which date had the highest low temperature? ______________ What was the temperature? __________