Section 1-3 Explore Real NumbersSPI 12A: Order a given set of rational numbersTPI 12F: Explore various representations of Absolute Value

Objectives:• Investigate the Real Number System • Classify and Compare Numbers

Natural Numbers

Real Number System

Whole Numbers

Integers

Rational NumbersIrrational Numbers

X

y

Real number line

Coordinate Plane

Natural Numbers

1, 2, 3, …1 2 3 4 5 6 7 8 9 10 11

Whole Numbers

0, 1, 2, 3, …0 1 2 3 4 5 6 7 8 9 10 11

Integers

. . . -3, -2, -1, 0, 1, 2, 3, … -3 -2 -1 0 1 2 3 4

Rational NumbersAny number that can be written

in the form where a and b are integers and b is not equal to 0.(Can be terminating, such as 6.27.. Or .. Repeating like 8.222….)

Irrational Numbers

Any number that can not be

written in the form of .(Nonrepeating & non-terminating)

Real Number System

a. - 3

b. 3.28

c.

d. .

Name the set of numbers to which each number belongs

Rational, integer

Rational

Irrational

Rational (its repeating)

1. Which set of numbers is most reasonable for displaying

outdoor temperatures? integers

ALGEBRA 1 LESSON 1-3ALGEBRA 1 LESSON 1-3 Practice: Determine the set of numbers that is reasonable for a given situation.

2. Which set of numbers is most reasonable for the number of

students who will go on a class trip? whole

3. Which set of numbers is most reasonable to determine the

height of a door? rational

4. Is the following statement true or false. If false, give a

counterexample. “All negative numbers are integers.”

False, because a negative number can be a fractionsuch as ½, which is not an integer.

Comparing Numbers and Ordering Fractions

Inequality: mathematical sentence that compares the value of 2 expressions.

a < b a is less than b a > b a is greater than b a = b a is equal to b a b a is less than or equal to b a b a is greater than or equal to b a ≠ b a is not equal to b

-1 -1/2 -1/8 0 3/4 1

Compare a set of rational numbers using a number line and inequalities. Write -1/8, 1, ¾, -1/2, -1 from least to greatest.

-1 < -1/2 < -1/8 < ¾ < 1

Step 1: Convert fraction by dividing numerator by denominator Step 2: Compare the decimals:

- the smaller number is the least (Pay attention to negative values)

Step 3: Convert back to fractions and write in order

Write 1/12, -2/3 amd -5/8 in order from least to greatest.

Step 1: Convert to decimal: 1/12 = .083 -2/3 = -.666666667 -5/8 = -.625

Step 2: Order decimals-.666666667 < -.625 < .083 Convert back to fraction-2/3 < -5/8 < 1/12

– = –0.75 Write each fraction as a decimal.

– = –0.583

– = –0.625

34

7 12

58

Write – , – , and – , in order from least to greatest.34

7 12

58

-0.75 < -0.625 < -0.583

Order Fractions by Converting to Decimals

Opposites• Two numbers that have the same distance from zero on a number line but lie in opposite directions

• Example: 1 and -1, 450 and -450, -1/2 and ½

Absolute Values• The distance of a number from zero on a number line

• Written as a number enclosed by 2 vertical lines

• Example: |3| and |-3| both have a value of 3

Absolute Values

-10 0 10

Home

Modeling Absolute ValueIf you are at home and decide to take a ride on your motorcycle to your friends house, which is ten miles away. Your friend lives in the red house.

How many miles did you travel away from your home?

You and your friend decide to go to the store, the yellow house. How far is it from your friends house to the store?

Find each absolute value.

a. |–2.5| b. |7|

–2.5 is 2.5 units from 0 on a number line.

7 is 7 units from 0 on a number line.

|–2.5| = 2.5 |7| = 7

c. |5 - 7|

-2 is 2 units from 0 on a number line.

|–2| = 2

Practice Absolute Value