Exponents: A quick short cut to

multiplication!

74 Means 7 x 7 x 7 x 7

Means 7 is used as a factor 4 times!

74

7 is the base4 is the exponentThe base is used as a factor 4 times.

Expanded notation:5 x 5 x 5 x 5 x 5 x 5

Exponential notation:

56

Evaluated Notation:

15,625

Exponents apply to fractions and decimals too!

2.474 means 2.47 x 2.47 x 2.47x 2.47 &

37.22098(½)4 means

½ x ½ x ½ x ½ &

-54 = ? (-5)4= ? Are they the same?Explain. -24 = ? (-2)4= ? Evaluate both.

(-5)4

Will this value be negative or positive?

(-5)3

Will this value be negative or positive?

Explain.

3 2 x 3 5

Means3 x 3 x 3 x 3 x 3 x 3 x 3

Can you see a short cut?Try it!

54 x 56 = ?27 x 26 =?

72 x 75

7 x 7 x 7 x 7 x 7 x 7 x 7Or77

823,543

We can do this with variables also!

w 3 w 2

w x w x w x w x w

w5

(2a2) (3a5)Apply the commutative property to re-arrange the elements of the

expression.

2 x 3 x a2 x a5 6a7

Power of a Power(63)4

Means this:63∙63∙63∙63

Or

612

(45)2

45 x 45 410

(52)4

52 x 52 x 52 x 52

58

65

63

62 What about this?

75 75-5 = 70

75

1

Therefore anything to the zero power equals

1.

Negative Exponents!5 -3 = 1 53

ab-2 = a b2

12 7 = 12 7-10 = 12-3 = 112 10 123

SCIENTIFIC NOTATION

A QUICK WAY TO WRITE REALLY, REALLY BIG

OR REALLY, REALLY SMALL NUMBERS.

Mathematicians

are Lazy!!!They decided that by

using powers of 10, they can create short versions of long

numbers.

Rules for Scientific Notation

To be in proper scientific notation the number must be written with* a number between 1 and 10* and multiplied by a power of

ten 23 X 105 is not in proper

scientific notation. Why?

Soooo137,000,000 can be

rewritten as

1.37 X 108

Now You TryUsing scientific notation,

rewrite the following numbers.

347,000.3.47 X 105

902,000,000.9.02 X 108

61,400.6.14 X 104

Convert these:

1.23 X 105

123,0006.806 X 106

6,806,000

Try These4,0004 X 103

2.48 X 103

2,4806.123 X 106 6,123,000306,000,0003.06 X 108

In the United States, 15,000,000 households use private wells for

their water supply. Write this number in scientific notation.

1.5 X 107

• The U.S. has a total of 1.2916 X 107 acres of land reserved for state parks. Write this in standard form.

12,916,000 acres

Why does a Negative Exponent give us a small

number? 10000 = 10 x 10 x 10 x 10 = 104 1000 = 10 x 10 x 10 = 103

100 = 10 x 10 = 102

10 = 101 1 = 100 Do you see a pattern?

Sooooo = 10-1

= = 10-2

= = 10-3

= = 10-4

101

1001

2101

10001

3101

100001

4101

Your TurnUsing Scientific Notation,

rewrite the following numbers.0.0008828.82 X 10-4

0.000000595.9 X 10-7

0.000044 X 10-5

Change to Standard Notation3.89 x 10-5

.0000389

5.074 x 10-9

.000000005074

6.125 x 107

61,250,000

More Examples1) 0.00044 X 10-4

2) 1.248 X 10-6

.0000012483) 6.123 X 10-5

.000061234) 0.000003063.06 X 10-6

5) 0.0008928.92 X 10-4

The nucleus of a human skin cell is about 7 X 10-6 meters in diameter. What is the length in standard notation?

.000007

A ribosome, another part of a cell, is about 0.000000003 of a meter in diameter. Write the length in scientific notation.

3 X 10-9

Metric System• Napoleon- to unite his empire• Used everywhere except U.S. • Based the number 10• Basic unit of length: meter• Basic unit weight: gram• Basic unit volume: liter

kilo hecto deka unit (meter or liter or gram) deci centi milliTo go down you multiply by ten for each step.To go up you divide by ten for each step.

Example:Change 7 kilometers to meters: • • = 7,000 meters