Section 2.10 notes.notebook
November 09, 2011
Section 2­10: Scientific Notation
Complete the tables.
Expression
8.7 x 101 = 8.7 x 10 8.7 x 102 = 8.7 x 100 8.7 x 103 = 8.7 x
Product
87 Expression Product 8.7 x 10­1 = 8.7 x 1
10 0.87 8.7 x 10­2 = 8.7 x 1
100 8.7 x 10­3 = 8.7 x 1. If 8.7 is multiplied by a positive power of 10, what relationship exists between the decimal point’s new position and the exponent?
2. When 8.7 is multiplied by a negative power of 10, how does the new position of the decimal point relate to the negative exponent?
scientific notation
a compact way of writing numbers with absolute values that are very large or very small
8.7 x 10­4
3.27 x 103
Changing from Scientific Notation to Standard Form:
­Multiplying by a positive power of 10 moves the
decimal point right.
­Multiplying by a negative power of 10 moves the decimal point left.
­The number of places the decimal point moves is the absolute value of the exponent. 1
Section 2.10 notes.notebook
November 09, 2011
Examples: 1. 7.42 x 105
2. 6.1 x 10­2
3. 3.714 x 102
4. 9.62 x 105
5. 2.85 x 10­6
Changing Standard Form to Scientific Notation:
­Move the decimal point so that the number is greater than or equal to one, but less than ten.
­Count the number of places you moved the decimal point to determine the value of the exponent.
­ If you moved the decimal point to the right, it is a negative exponent. If you moved the decimal point to the left, it is a positive exponent.
2
Section 2.10 notes.notebook
November 09, 2011
Examples:
6. 14,140,000
7. 0.00876
8. 0.114
9. ­931,500,000
10. 0.00443
11. The table below lists the total value of music shipments for four years. List the years from least to greatest dollar amount.
Year
Music Shipments ($)
2003
1.19 x 1010
2004
1.23 x 1010
2005
1.22 x 1010
2006
1.15 x 1010
3
Section 2.10 notes.notebook
November 09, 2011
12. The areas of the world’s oceans are listed in the table. Order the oceans according to their area from least to greatest.
Ocean
Area (mi2)
Atlantic
2.96 x 107
Arctic
5.43 x 106
Indian
2.65 x 107
Pacific
6.0 x 107
Southern
7.85 x 106
13. Determine whether 1.2 x 105 or 1.2 x 106 is closer to one million.
14. Arrange these numbers in increasing order.
216,000,000; 2.2 x 103; 3.1 x 107; 310,000
4