Intermediate Algebra (11th edition)

Using Scientific Notation in Computation

Evaluate.

Express all numbers in scientific notation.

Commutative property

Product rule

Quotient rule

Simplify.

Write 0.2 in scientific notation.

Product rule

= 2000 Standard notation NOW TRY

= 2 * 103

= 12 10 -^12 104

=0.2* 104

=

1.92* 1.5

3.2* 4.5

* 104

=

1.92 1.5 103

3.24.5 10 -^1

=

1.92 1.5 106 * 10 -^3

3.2 4.5 10 -^5 * 104

=

1.92 106 1.5* 10 -^3

3.2 10 -^5 4.5* 104

1,920,000*0.0015

0.000032* 45,000

EXAMPLE 11

SECTION 5.1 Integer Exponents and Scientific Notation 273

Don’t stop

here!

Using Scientific Notation to Solve Problems

In 1990, private health care expenditures in the United States were $427 billion. By

2006, this figure had risen by a factor of 2.7— that is, it had risen by over times in

only 16 yr. (Source:U.S. Centers for Medicare & Medicaid Services.)

(a)Write the 1990 health care expenditure in scientific notation.

Write 427 in scientific notation.

Product rule

In 1990, the expenditure was

(b)What were expenditures in 2006?

Multiply the result in part (a) by 2.7.

Commutative and associative properties

Multiply.

Write 11.529 in scientific notation.

Product rule

Expenditures in 2006 were about $1,152,900,000,000 (over $1.1 trillion).

NOW TRY

= 1.1529* 1012

= 1 1.1529 1012 1011

= 11.529* 1011

= 1 2.7 4.27 2 1011

1 4.27 10112 2.7

$4.27* 1011.

=4.27 * 1011

= 1 4.27 1022 109

= 427 * 109 1 billion=1,000,000,000= 109

427 billion

(^2 12)

EXAMPLE 12

NOW TRY
EXERCISE 11
Evaluate.

0.00063*400,000

1400 *0.000003

NOW TRY
EXERCISE 12
The speed of light is approxi-
mately 30,000,000,000 cm per
sec. How long will it take
light to travel 1.2* 1015 cm?

NOW TRY ANSWERS
11.60,000
12.4.0* 104 sec,or 40,000 sec

NOTEWhen converting from scientific notation to standard notation, use the expo-

nent to determine the number of places and the direction in which to move the

decimal point.