Embed Size (px)
Citation preview
8.3
Scientific Notation
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.
HANDOUT
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
= 0.00000481
The decimal point moved 6 places to the left.
= 4.81 × 0.000001= 4.81 × 610
1
Scientific 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.
Use these steps to express a number of the forma × 10n in standard notation:
HANDOUT
Express in standard notation.
move decimal point 3 places to the left.
Answer: 0.00748
Answer: 219,000
Express in standard notation.
move decimal point 5 places to the right.
Express each number in standard notation.
a.
b.
Answer: 0.0316
Answer: 7610
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.
Use these steps to express a number in scientific notation:
Express 0.000000672 in scientific notation.
Move decimal point 7 places to the right.
and
Answer:
Express 3,022,000,000,000 in scientific notation.
Move decimal point 12 places to the left.
Answer:
and
Express each number in scientific notation.
a. 458,000,000
b. 0.0000452
Answer:
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
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:
Write each of these numbers in scientific notation.
Answer: Shoes sold to women:
Shoes sold to men:
Total spent:
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 thecirculation 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
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: The Wall Street Journal: USA Today: The New York Times:
Scientific Notation
You can use scientific notation to simplify computation with very large and/or very small numbers.
Evaluate Express the result in scientific and standard notation.
Commutative and Associative Properties
Product of Powers
Associative Property
Product of Powers
Answer:
Evaluate Express the result in scientific and standard notation.
Answer:
Evaluate Express the result in scientific
and standard notation.
Associative Property
Product of Powers
Answer:
Evaluate Express the result in scientific
and standard notation.
Answer:
Practice Problems
Page: 428
Problems: 19-55
