1. Algebra 8-3 Scientific Notation
Math Pacing
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2. Algebra 8-3 Scientific Notation
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3. Algebra 8-3 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.
8-3 Scientific Notation
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4. Algebra 8-3 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.
8-3 Scientific Notation
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5. Algebra 8-3 Scientific Notation
Examples
6.59 × 104
= 6.59 × 10,000
= 65,900
The decimal point moved 4 places to the right.
= 4.81 ×
4.81 × 10– 6
= 4.81 × =
The decimal point moved 6 places to the left.
8-3 Scientific Notation
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6. Algebra 8-3 Scientific Notation
Use these steps to express a number of the form a × 10n in standard notation:
Determine whether n > 0 or n < 0.
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.
Add zeros, decimal point and/or commas as needed to indicate place value.
8-3 Scientific Notation
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7. Scientific to Standard Notation
Express in standard notation.
move decimal point 3 places to the left.
Answer:
Example 3-1a

8. Scientific to Standard Notation
Express in standard notation.
move decimal point 5 places to the right.
Answer: 219,000
Example 3-1b

9. Scientific to Standard Notation
Express each number in standard notation. a. b.
Answer:
Answer: 7610
Example 3-1c

10. Algebra 8-3 Scientific Notation
Use these steps to express a number in scientific notation:
Move the decimal point so that it is to the right of the first nonzero digit. The result is a decimal number a.
Observe the number of places n and the direction in which you moved the decimal point.
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.
8-3 Scientific Notation
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11. Standard to Scientific Notation
Express in scientific notation.
Move decimal point 7 places to the right.
and
Answer:
Example 3-2a

12. Standard to Scientific Notation
Express 3,022,000,000,000 in scientific notation.
Move decimal point 12 places to the left.
and
Answer:
Example 3-2b

13. Standard to Scientific Notation
Express each number in scientific notation.
a. 458,000,000 b
Answer:
Answer:
Example 3-2c

14. Algebra 8-3 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
8-3 Scientific Notation
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15. 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:
Example 3-3a

16. Use Scientific Notation
Write each of these numbers in scientific notation.
Answer: Shoes sold to women:
Shoes sold to men:
Total spent:
Example 3-3b

17. Use Scientific Notation
The average circulation for all U.S. daily newspapers in 2000 was 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
Example 3-3c

18. Use Scientific Notation
The average circulation for all U.S. daily newspapers in 2000 was 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:
Example 3-3d

19. Algebra 8-3 Scientific Notation
You can use scientific notation to simplify computation with very large and/or very small numbers.
8-3 Scientific Notation
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20. 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:
Example 3-4a

21. Multiplication with Scientific Notation
Evaluate Express the result in scientific and standard notation.
Answer:
Example 3-4c

22. Division with Scientific Notation
Evaluate Express the result in scientific and standard notation.
Associative Property
Product of Powers
Answer:
Example 3-5a

23. Division with Scientific Notation
Evaluate Express the result in scientific and standard notation.
Answer:
Example 3-5b