Download Student Notes, Section 1

Student Notes, Section 1.7
Scientific Notation
A number is in scientific notation when it is in the form N  10 m , where N is an integer or
decimal form, 1  N  10 , and m is an integer.
If m  0 , the number is larger than zero. If m < 0, the number is less than zero.
A
Writing numbers in scientific notation or finding a number from scientific
notation
1)
In 1990 the National Health Care expenditures was $695,600,000,000. (Source:
U.S. Centers for Medicare and Medicaid Services) Write this in scientific notation.
2)
President Bush's budget plan for 2003 was $2.128  10 . (Source: The Gazette,
February 5, 2002) Write as a standard number.
12
3)
A grain of sand can weight as little as 0.0648 grams. (Source: textbook, p. 61)
Write this weight in scientific notation.
B
Rounding and Significant Digits
When two or more measurements written in scientific notation are multiplied or divided,
the result should be rounded so that it has the same number of significant digits as the
measurement with the fewest significant digits. Always round at the end of calculations.
Significant digits
 43,200 has 3 significant digits
 0.0032 has 2 significant digits
 4.10 has 3 significant digits
 4.506  10 4 has 4 significant digits
D
Multiplication/Division with Scientific Notation
Multiply or Divide and give answer using the correct number of significant digits.
1)
(7.0  1012 )(3.0  10 8 )
2)
4.8  10 3
4.0  10 5
3)
(2.31  10 2 )mm  (3.1 10 2 )mm
4)
(4.2  10 5 )(6.1  10 3 )
5)
1.26  10 9
4.0  10 5
6)
(4.0  10 2 )(3.2  10 3 )
3.1  10 8
D
Application Problems
1)
On October 28, 1998 an IBM computer could perform 3.9  10 8 operations per
second. This was 15,000 times faster than the normal desktop computer at the time.
How many operations per second would a normal computer perform?
(Source: IBM)
2)
The average distance from earth to the sun is 9.3  10 7 miles. How long would it
take a rocket traveling 2.9  10 3 miles per hour to reach the sun, if this was possible?
3)
A light year is approximately 5.88  1012 miles. If the diameter of the Milky Way
galaxy is about 5.88  1017 miles, how many light years is it from one end of the galaxy to
the other?
4)
An average of 4.55  1011 bacteria lives in a pound of mud in the U.S. (Source:
Harper's Magazine, April 1996, p. 13) There are 16 ounces in a pound. If 6.0 teaspoons
are in an ounce and 60 drops are in a teaspoon, how many bacteria live in a drop of mud?