1.3 Exploring 1.3 Exploring Real NumbersReal Numbers

Textbook pg 17Textbook pg 17

TerminologyTerminology• Natural Numbers: {1, 2, 3, 4, 5, 6,…}• Whole Numbers: {0, 1, 2, 3, 4, 5,…}• Integers: {…,-3, -2, -1, 0, 1, 2, 3, …}• A Rational Number is any number that

can be written in the form where b≠0 and a and b are integers, or as a terminating or repeating decimal.

b

a

• An Irrational Number is any number that cannot be written in the form where b≠0 and a and b are integers, or as a terminating or repeating decimal.

• Together, rational and irrational numbers for the set of Real Numbers.

b

a

Real Numbers

Rational Numbers Irrational Numbers

Integers

Whole Numbers

Any example that proves a Any example that proves a statement false is a statement false is a CounterexampleCounterexample..

– All odd numbers end in 3– Counter example: 25

To find the Opposite of a To find the Opposite of a number, change its sign.number, change its sign.

• The opposite of positive is negative– The opposite of 3 is -3

• The opposite of negative is positive– The opposite of -10 is 10

Absolute ValueAbsolute Value• A number’s absolute value is its

distance away from Zero on the number line

• Absolute Value is ALWAYS positive because you cannot have negative distance

Find Each Absolute ValueFind Each Absolute Value

4 12 )5

46 )4

2

1 )3

21 )2

4 )1

-

= 4

= 21

= ½

= 2

= 48

An Inequality is a mathematical sentence that compares the value of two expressions

using an inequality symbol such as:

• ‹

• ›• ≤ • ≥ • ≠

Less Than

Greater Than

Less Than OR Equal To

Greater Than OR Equal To

Not Equal To

Comparing Using Comparing Using InequalitiesInequalities

83.7 11.3 )4

19- 19 )36

1

3

2 )2

6

1

3

2 )1

›

‹=

‹

Assignment # 3Assignment # 3• Beginning on textbook page 20• Problems 42-63 all, 68-72 all, 79-85

all, 87-95 odd• Write all problems except for the

word problems. Show all of your work.

• Do not pack up until instructed to do so by the teacher.