Converting a Decimal to Scientific Notation

1. Count the number N of places that the decimal point must be moved in order to arrive at a number x, where 1 < x < 10.

2. If the original number is greater than or equal to 1, the scientific notation is If the original number is between 0 and 1, the scientific notation is

x N10 .

x N 10 .

Examples: Scientific Notation

Write the number 5,100,000,000 in scientific notation.

Solution: 51 109.

Write the number 0.00032 in scientific notation.Solution: 3 2 10 4.

Write as a decimal.5103.4

Solution: 0.000043

Exponents: Basic Definitions

If a is a real number and n is a positive integer,

a a a an

n

factors

a a0 1 0 if

aa

ann

1 0 if

Examples:

4 4 4 43

6 10

4 14

33

Using your calculator

For Scientific Calculators:

Evaluate: 4(3.4)

Keystrokes: 3.4 yx 4 =133.6336

For Graphing Calculators:

Evaluate: 4(3.4)Keystrokes: 3.4 4 =

133.6336^

Converting a Decimal to Scientific Notation

1. Count the number N of places that the decimal point must be moved in order to arrive at a number x, where 1 < x < 10.

2. If the original number is greater than or equal to 1, the scientific notation is If the original number is between 0 and 1, the scientific notation is

x N10 .

x N 10 .

Examples: Scientific Notation

Write the number 5,100,000,000 in scientific notation.

Solution: 51 109.

Write the number 0.00032 in scientific notation.Solution: 3 2 10 4.

Write as a decimal.5103.4

Solution: 0.000043

Stop for 7Stop for 7thth grade grade

Laws of Exponents

a a a a a ab a b

aa

aa

a

ab

ab

b

m n m n m n mn n n n

m

nm n

n m

n n

n

if

if

1 0

0

ab

ba

a bn n

if 0 0,

Example:

Simplify the expression. Express the answer so only positive exponents occur.

3 2 4

3

2x yx y

3 2 3 4 1 2x y

3 1 3 2x y

3 2 1 2 3 2

x y 3 2 2 6x y xy

2

69

Example:

Write so that all exponents are positive.x yx y

3 2

1 4

x yx y

xx

yy

3 2

1 4

3

1

2

4

x y3 1 2 4( )

x y4 6 xy

4

6