Chapter 8 - Exponents

Scientific Notation

Mental MathMultiplying: Move the decimal to the right

47 x 10

82 x 100

2 583 x 100

758 91 x1000

470

8200

258.3

758910

“Bigger”

Mental MathDividing: Move the decimal to the left

9250 ÷ 10

82 ÷ 100

2 583 ÷ 100

7589 1 ÷ 1000

925

.82

0.02583

7.5891

“Smaller”

Scientific Notation

must be

__

a

___ _

sing

____ ... 1

l

is

e

non

any inte

-zero digit

1,2,3,4,5,6,7,8,9

0

ger

. n

n

_____

Base of 10

8.5 Scientific NotationExamples: numbers into correct scientific notation.

38,700,000 3 87.7

706,000 7 06.5

4035 4 035.3

If it is a whole number, then the exponent is positive.

10

10

10

8.5 Scientific NotationExamples: numbers into correct scientific notation.

.0000000706 7 06. 8

.00000081 8 1. 7

.000009 9 6

If it is a decimal, then the exponent is negative.

10

10

10

8.5 Scientific Notation

2 61.4 310 10

1.4 3 2 610 10

Multiply

4.2 810

8.5 Scientific Notation

4 20.4 010 .6 10

0.4 0.6 4 210 10

Multiply

0.24 610

2 4. 10 5

8.5 Scientific Notation

4 31.4 7.610 10

1.4 7.6 4 310 10

Multiply

10.64 710

1 064. 106

3

11

1.2

4

10

1.8 0

1.2

4.8

3

11

10

10

0.25 3 1110

0.25 810

2.5 10 7

8.5 Scientific NotationExamples: computing with scientific notation

2 3 310 101.2 5 2. 104

Group number factors together and group powers of 10 together.

2 3 3101.2 10 105 2.4

14.4

1 44.

210310

Examples: computing with scientific notation

2

6

5

8

10

10

Group quotient numbers together and group powers of 10 together.

2

6

1

8 10

5 0

0.6256.25

10 4

10 3