Algebra 1 Common Core Student Edition, Grade 8-9

An in e q u a lity is a mathematical sentence that compares the values of two expressions

using an inequality symbol. The symbols are

<, less than

> , greater than

s, less than or equal to

greater than or equal to

How can you

compare numbers?

Write the numbers in

the same form, such as

decimal form.

Pr o b l em 4 Co m p ar i n g Real N u m b er s

What is an inequality that compares the numbers V l 7 and 4^?

Vl7 = 4.12310 ... W rite the square root as a decimal.

1 —

W rite the fraction as a decimal.

Compare using an inequality symbol.

41 = 4.3

Vl7 < 4^

(§J ^ Got It? 4. a. What is an inequality that compares the numbers V I29 and 11.52?

b. Reasoning In Problem 4, is there another inequality you can write that

compares the two numbers? Explain.

W h y is i t u s efu l to
rew rite numbers in
decimal form?
It allows you to compare
numbers whose values
are close, like 1 and 0.26.

You can graph and order all real numbers using a number line.

Grap h in g an d Ord erin g Real N um b ers

Multiple Choice What is the order of Vi, 0.4, - |, V2, and — 1.5 from least

to greatest?

CD -§,0.4, -1.5, V2, V i

C D —1.5, V2, 0.4, Vi, —§

CD -1.5, -§,0.4, V 2 , V i

CD Vi, V2, 0.4, -§ , -1.5

Five real numbers Order of numbers

from least to

greatest

Graph the numbers on

a number line.

First, write the numbers that are not in decimal form as decimals: V i = 2, —§ ~ —0.67,

and V 2 ~ 1.41. Then graph all five numbers on the number line to order the numbers,

and read the graph from left to right.

• 
  
  
  
  1. 5 3 0. 4 V 2 V 4
     I • l « — I » - I ■»•■■■» h
     -2 -1 0 1
  
  
  
  

From least to greatest, the numbers are -1.5, —§, 0.4, V2, and Vi. The correct

answer is C.

Go t It? 5. Graph 3.5, —2.1, V9, —§, and V 5 on a number line. What is the order of

the numbers from least to greatest?

L

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Lesson 1-3 Real N u m b er s an d t h e N u m b er Li n e 19