2.1 THE REAL #S AND

ABSOLUTE VALUE

Objective: Compare real numbers.Standards Addressed: 2.1.8.C:

Distinguish between and order rational and irrational numbers.

2.1.8.F: Use the number line model to demonstrate integers and their

applications.

THE REAL NUMBERS: Natural numbers (N) 1, 2, 3, …. Whole numbers (W) 0, 1, 2, 3, …. Integers (Z) …, -3, -2, -1, 0, 1, 2, 3, … Rational numbers (Q) p/q, where p and q

are integers and q ≠ 0. Terminating (2.77) &

repeating (1/3) Irrational numbers (I) #s whose decimal

part doesn’t terminate or repeat (i.e. ∏ )

Real numbers (R) all rational & irrational #s

EX.1 a. 0

R, Q, Z, W

b. ½ R, Q

c. -8 R, Q, Z

d. 8 R, Q, Z, W, N

e. R, I

EX.2 USE DIVISION TO WRITE EACH RATIONAL # AS A DECIMAL & INDICATE WHETHER THE # IS A TERMINATING DECIMAL OR A REPEATING DECIMAL.

a. 4/5

b. 4/11

c. 5/8

d. 7/9

e. 5/12

f. ¾

Terminating

Terminating

Repeating

Repeating

Repeating

Terminating

THE SYMBOLS USED TO COMPARE 2 REAL #S ARE STATED & EXPLAINED BELOW:

< is less than or equal to

> is greater than or equal to

EX. 3

OPPOSITES On the # line, 2 #s that lie on opposite

sides of 0, and are the same distance from 0 are opposites.

The opposite of a negative # is always a positive #.

The opposite of zero is zero itself.

EX. 4 EVALUATE EACH EXPRESSION.

EX. 5 ABSOLUTE VALUE

7 14.2

0 13