Beginning Algebra, 11th Edition

Using Scientific Notation to Solve an Application

In 2008, the national debt was (which is more than $10 trillion). The

population of the United States was approximately 304 million that year. About how

much would each person have had to contribute in order to pay off the national debt?

(Source: Bureau of Public Land; U.S. Census Bureau.)

Write the population in scientific notation. Then divide to obtain the per person

contribution.

Quotient rule

Divide. Round to 5 decimal places.

Write without exponents.

Each person would have to pay about $32,977. NOW TRY

=32,977

=0.32977* 105

=

1.0025

3.04

* 105

1.0025* 1013

304,000,000

=

1.0025* 1013

3.04* 108

$1.0025* 1013

EXAMPLE 5

SECTION 5.3 An Application of Exponents: Scientific Notation 315

In 1935, Charles F. Richter devised a scale to compare the intensities of earthquakes.

The intensityof an earthquake is measured relative to the intensity of a standard zero-

levelearthquake of intensity The relationship is equivalent to where

Ris the Richter scalemeasure.

For example, if an earthquake has magnitude 5.0 on the Richter scale, then its

intensity is calculated as

which is 100,000 times as intense as a zero-level earthquake.

I=I 0 10 5.0= I 0 100,000,

I 0. I=I 0 * 10 R,

CONNECTIONS

Write 304 million in

scientific notation.

For Discussion or Writing

Source: U.S. Geological Survey.

Year Earthquake Location Richter Scale Measurement

1964 Prince William Sound, Alaska 9.2

2004 Sumatra, Indonesia 9.0

2007 Central Peru 8.0

2008 E. Sichuan Province, China 7.9

2002 Hindu Kush, Afghanistan 5.9

NOW TRY
EXERCISE 5
The land area of California is
approximately ,
and the 2008 estimated popu-
lation of California was
approximately people.
Use this information to
estimate the number of square
miles per California resident
in 2008. (Source:U.S. Census
Bureau.)

4 * 107

1.6* 105 mi^2

I 0 × 100 I 0 × 101 I 0 × 102 I 0 × 103 I 0 × 104 I 0 × 105 I 0 × 106 I 0 × 107 I 0 × 108

012345678

Intensity

Richter Scale

To compare two earthquakes, a ratio of the intensities is calculated. For example,

to compare an earthquake that measures 8.0 on the Richter scale with one that meas-

ures 5.0, find the ratio of the intensities.

Therefore, an earthquake that measures 8.0 on the Richter scale is 1000 times as intense

as one that measures 5.0.

intensity 8.0

intensity 5.0

=

I 0 * 10 8.0

I 0 * 10 5.0

=

108

105

= 108 -^5 = 103 = 1000

NOW TRY ANSWER

5. 4 * 10 -^3 mi^2 , or 0.004 mi^2