Title: Lesson 3-3
Author: mark_cameron
Last saved by: MHE
Company: McGraw-Hill

Lesson 3-4

EXAMPLES   Classify Numbers
Name all sets of numbers to which each real number belongs. belongs.
1.  0.32323232…
The decimal ends in a repeating pattern. It is a rational number because it is equivalent to .

2. 
Since = 5, it is a whole number, an integer, and a rational number.

3.  
 ≈ 2.828427125… Since the decimal does not terminate or repeat, it is an irrational number.

Example 4  Graph Real Numbers
Estimate  and −to the nearest tenth. Then graph  and − on a number line.

Use a calculator to determine the approximate decimal values.
 ≈ 2.236067977…
− ≈ −1.414213562…
 ≈ 2.2 and − ≈ −1.4. Locate these points on the number line.

EXAMPLES Compare Real Numbers 
Replace each ● with <, >, or = to make a true sentence.
5.  ● 3

Write each number as a decimal.
3.16227766…

Since 3.16227766… is greater than 3.1,  > 3.

6. 1. ● 

Write  as a decimal.
= 1.6
1. = 1.666666666…
Since 1.66666666… is greater than 1.6, 1. > .

Example 7  Real-World Example
DRIVING  When a car brakes suddenly, it leaves skid marks. The formula to calculate how fast the car was traveling is S =  where S is the speed of the car and D is the length of the skid mark. If Ellie’s car left a 35-foot skid mark and Adam’s car left a 45-foot skid mark, how much faster was Adam traveling?

Use a calculator to approximate how fast each person was traveling.
Ellie:  		Adam:  

Adam was traveling about 36.74 – 32.40 or 4.34 miles per hour faster than Ellie.