the real numbers and absolute value section 2.1. irrationalsrationals integers whole natural real...

THE REAL NUMBERS AND ABSOLUTE VALUE

SECTION 2.1

IrrationalsRationals

Integers

Whole

Natural

2

3

.75

5

3

102 0

4

5.34

.14923...

8

1 25

Real Numbers

( _______ , ___________)

Irrational numbers – Decimal that never ________ and never ____________.

Real numbers – the set of both ____________ and _______________ numbers.

rational

irrational

endsrepeats

Rational numbers – Any number that can be written as a decimal that either ___________ or ___________________.ends repeats

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

( ___________ , _________, ___________)negatives zero positives

Whole numbers -

0,1, 2, 3, 4,...

( _______ , ____________)zero postives

Natural numbers -

1, 2, 3, 4,...

( _____________ )postives

negatives positiveszero

0 1 2 3 4-1-2-3-4

Symbols used for ordering numbers:

Less than

greater than

Equal to

Less than or equal to

greater than or equal to

Example 1: Insert an ordering symbol to make each statement true.

5 ____ 71 8______

2 16

4.8 ___ 4.7 24 ____ 63

Try these….

3 ___ 6 8.5 ___ 8.6

1 3___

2 537 ____ 97

A. B.

C. D.

On the number line, two numbers that lie on opposite sides of 0 and are the same _______________ from 0 are called ______________.

distanceopposites

8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8

The opposite of 6 is _____.

The opposite of -3 is _____.

-6

3

3 3

When finding the opposite of any number, use the opposite symbol.

6 opposite

6 6

opposite 3

The opposite of a positive is always __________.The opposite of a negative is always __________.The opposite of zero is always _______.

negativepositive

zero

Example 2: Evaluate each expression:

2

3

0

7.4 3.2

A.

B.

C.

2

3

0

4.2

Try these…

4

7

0

6.2 2.7

D.

E.

F.

4

7

0

3.5

x x

The ________________ of a real number is the distance it is from ________ on a number line.

means the absolute value of The symbol

absolute valuezero

Example 3: Simplify:

7 14.2 0 9 4 A. B. C. D.

7 14.2 0 13

13

13

7.3

8 3

Try these…

F.

G.

E. 13

7.3

5 5