Scientific Notation
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1
4
2
49
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25
4
2 :1
n
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1
n
4
2
6
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3x y
8
2
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3
8
6
x y
2
Scientific Notation
Scientific Notation
When dealing with very large or very small
numbers, keeping track of place value can be
difficult.
For this reason, numbers such as these are often
expressed in scientific notation.
Scientific Notation
Scientific Notation
A number is expressed in scientific notation when
it is written as a product of a factor and a power of
10. The factor must be greater than or equal to 1
and less than 10.
A number in scientific notation is written as
a × 10n, where 1 ≤ a < 10 and n is an integer.
Scientific Notation
6.59 × 104
Examples
= 6.59 × 10,000
= 65,900
The decimal point moved 4 places to the right.
4.81 ×
10– 6
= 4.81 ×
1
10
6
= 4.81 × 0.000001
= 0.00000481
The decimal point moved 6 places to the left.
Scientific Notation
Use these steps to express a number of the form
a × 10n in standard notation:
1. Determine whether n > 0 or n < 0.
2. If n > 0, move the decimal point in a to the right n
places.
If n < 0, move the decimal point in a to the left n
places.
3. Add zeros, decimal point and/or commas as needed
to indicate place value.
Scientific to Standard Notation
Express
in standard notation.
move decimal point 3
places to the left.
Answer: 0.00748
Scientific to Standard Notation
Express
in standard notation.
move decimal point 5
places to the right.
Answer: 219,000
Scientific to Standard Notation
Express each number in standard notation.
a.
Answer: 0.0316
b.
Answer: 7610
Scientific Notation
Use these steps to express a number in scientific
notation:
1. Move the decimal point so that it is to the right of
the first nonzero digit.
The result is a decimal number a.
2. Observe the number of places n and the direction in
which you moved the decimal point.
3. If the decimal point moved to the left,
write as a × 10n.
If the decimal point moved to the right,
write as a × 10– n.
Standard to Scientific Notation
Express 0.000000672 in scientific notation.
Move decimal
point 7 places
to the right.
and
Answer:
Standard to Scientific Notation
Express 3,022,000,000,000 in scientific notation.
Move decimal point
12 places to the left.
and
Answer:
Standard to Scientific Notation
Express each number in scientific notation.
a. 458,000,000
Answer:
b. 0.0000452
Answer:
Scientific Notation
You will often see large number in the media
written using a combination of a number and a
word, such as 3.2 million.
To write this number in standard notation, rewrite
the word million as 106.
The exponent 6 indicates that the decimal point
should be moved 6 places to the right.
3.2 million = 3,200,000
Use Scientific Notation
The Sporting Goods Manufacturers
Association reported that in 2000,
women spent $4.4 billion on 124
million pairs of shoes. Men spent $8.3
billion on 169 million pairs of shoes.
Express the numbers of pairs of shoes sold to
women, pairs sold to men, and total spent by both
men and women in standard notation.
Answer: Shoes sold to women:
Shoes sold to men:
Total spent:
Use Scientific Notation
Write each of these numbers in scientific notation.
Answer: Shoes sold to women:
Shoes sold to men:
Total spent:
Use Scientific Notation
The average circulation for all U.S. daily newspapers
in 2000 was 111.5 billion newspapers. The top three
leading newspapers were The Wall Street Journal,
with a circulation of 1.76 million newspapers, USA
Today, which sold 1.69 million newspapers, and The
New York Times, which had 1.10 million readers.
a. Express the average daily circulation and the
circulation of the top three newspapers in
standard notation.
Answer: Total circulation: 111,500,000,000; The Wall
Street Journal: 1,760,000; USA Today: 1,690,000; The
New York Times: 1,100,000
Use Scientific Notation
The average circulation for all U.S. daily newspapers
in 2000 was 111.5 billion newspapers. The top three
leading newspapers were The Wall Street Journal,
with a circulation of 1.76 million newspapers, USA
Today, which sold 1.69 million newspapers, and The
New York Times, which had 1.10 million readers.
b. Write each of the numbers in scientific notation.
Answer: Total circulation:
Journal:
USA Today:
The New York Times:
The Wall Street
Scientific Notation
You can use scientific notation to simplify
computation with very large and/or very
small numbers.
Multiplication with Scientific Notation
Evaluate
Express the result in
scientific and standard notation.
Commutative and
Associative Properties
Product of Powers
Associative Property
Product of Powers
Answer:
Multiplication with Scientific Notation
Evaluate
Express the result in
scientific and standard notation.
Answer:
Division with Scientific Notation
Evaluate
Express the result in scientific
and standard notation.
Associative Property
Product of Powers
Answer:
Division with Scientific Notation
Evaluate
Express the result in scientific
and standard notation.
Answer: