1. a x 10n, Scientific Notation Scientific Notation
A number written in the form
a x 10n,
where n is an integer and a is greater than or equal to 1 and less than 10, is said to be in scientific notation.

2. Writing a Number in Scientific Notation
Step 1 Move the decimal point to the right of the first nonzero digit.
Step 2 Count the number of places you moved the decimal point. The number of places is the absolute value of the exponent on 10.
Step 3 If the original number was “large” (10 or more), the exponent on 10 is positive. If the number was “small” (between 0 and 1), the exponent is negative.

3. Writing Numbers in Scientific Notation
EXAMPLE Writing Numbers in Scientific Notation
Write each number in scientific notation.
( a ) 470,000,000
= x 108
= x 10n
Step 1 Move the decimal point to the right of the first nonzero digit.
Step 2 Count the number of places you moved the decimal point.
Step 3 The original number was “large” so the exponent is positive. .
Move the decimal point 8 places.

4. Writing Numbers in Scientific Notation
EXAMPLE Writing Numbers in Scientific Notation
Write each number in scientific notation.
( b )
= x 10n
= x 10– 5
Step 1 Move the decimal point to the right of the first nonzero digit.
Step 2 Count the number of places you moved the decimal point.
Step 3 The original number was “small” so the exponent is negative. .
Move the decimal point 5 places.

5. Writing Numbers in Scientific Notation
EXAMPLE Writing Numbers in Scientific Notation
Write each number in scientific notation.
( c )
= x 10n
= x 10– 10
9 zeroes
Step 1 Move the decimal point to the right of the first nonzero digit.
Step 2 Count the number of places you moved the decimal point.
Step 3 The original number was “small” so the exponent is negative. .
Move the decimal point 10 places.

6. Writing Numbers in Scientific Notation
EXAMPLE Writing Numbers in Scientific Notation
Write each number in scientific notation.
( d ) 5,100,000,000,000,000,000
= x 10n
= x
Step 1 Move the decimal point to the right of the first nonzero digit.
Step 2 Count the number of places you moved the decimal point.
Step 3 The original number was “large” so the exponent is positive. .
Move the decimal point 18 places.

7. Converting Scientific Numbers to Numbers without Exponents
To convert a number written in scientific notation to a number without exponents, remember that multiplying by a positive power of 10 will make the number larger; multiplying by a negative power of 10 will make the number smaller.

8. Writing Numbers without Exponents
EXAMPLE Writing Numbers without Exponents
Write each number without exponents.
( a ) x 104
Since the exponent is positive, make 9.2 larger by moving the
decimal point 4 places to the right, inserting zeros as needed.
9.2 x =
= ,000

9. Writing Numbers without Exponents
EXAMPLE Writing Numbers without Exponents
Write each number without exponents.
( b ) x 107
Since the exponent is positive, make 5.38 larger by moving the
decimal point 7 places to the right, inserting zeros as needed.
5.38 x =
= ,800,000

10. Writing Numbers without Exponents
EXAMPLE Writing Numbers without Exponents
Write each number without exponents.
( c ) x 10– 5
Move 5 places to the left; multiplying by a negative power
of 10 makes the number smaller.
6.17 x 10– = =

11. The Exponent
NOTE
As shown in Example 2, the exponent tells the number of places and the direction that the decimal point is moved.
Positive exponents move the decimal point to the right.
5.38 x = ,800,000
Negative exponents move the decimal point to the left.
6.17 x 10– =

12. Multiplying and Dividing with Scientific Notation
EXAMPLE Multiplying and Dividing with Scientific Notation
Write each product or quotient without exponents.
( a ) ( 5 x ) ( 7 x 10– 2 )
= ( 5 x 7 ) ( x 10– 2 )
Commutative & associative properties
= x 106
Product rule for exponents
= 35,000,000
Write without exponents.

13. Multiplying and Dividing with Scientific Notation
EXAMPLE Multiplying and Dividing with Scientific Notation
Write each product or quotient without exponents.
( b )
( 8 x 10 – 6 )
( 4 x ) = 8 4
10– 6
10 2 x
= x 10– 8 =

14. Solving an Application Problem
EXAMPLE Solving an Application Problem
Pluto is approximately 6 x 109 miles from the sun. The speed of light
is approximately 3 x 105 km/s. How many hours does it take for light
to travel from the sun to Pluto?
( 6 x )
( 3 x ) = 6 3
109
105 x
= x 104
= ,000 hours
≈ years!

15. Solving an Application Problem
EXAMPLE Solving an Application Problem
A standard piece of paper is approximately inches. How thick
would 1,000 pieces of paper be?
( x 10– 3 ) ( 1 x )
= ( x 1 ) ( 10– 3 x )
= x 100
= x 1
= 3.8 inches

16. Solving an Application Problem
EXAMPLE Solving an Application Problem
In 2008, Warren Buffet was worth about $62,000,000,000. If he
decided to give all of his money away, how many millionaires could
he make?
( x )
( 1 x ) =
6.2 1
1010
106 x
= x 104
= 62,000 millionaires