OBJECTIVES
Basic Concepts
In scientific notation, there is always one nonzero digit before the decimal point.
Decimal point moves 1 place to the right.
Decimal point moves 2 places to the right.
Decimal point moves 3 places to the right.
Decimal point moves 1 place to the left.
Decimal point moves 2 places to the left.
Decimal point moves 3 places to the left.NOTE In work with scientific notation, the times symbol, is commonly used.
A number in scientific notation is always written with the decimal point after the
first nonzero digit and then multiplied by the appropriate power of 10.For example,
56,200 is written since
Other examples include
42,000,000 written
0.000586 written
and 2,000,000,000 written
To write a number in scientific notation, follow these steps. (For a negative number,
follow these steps using the absolute valueof the number. Then make the result negative.)
2 * 109.
5.86* 10 -^4 ,
4.2* 107 ,
56,200=5.62 10,000=5.62 104.
5.62* 104 ,
*,
3.19 10 -^3 = 3.19 0.001= 0.00319
3.19 10 -^2 = 3.19 0.01=0.0319
3.19 10 -^1 = 3.19 0.1= 0.319
3.19 103 = 3.19 1000 =3190.
3.19 102 = 3.19 100 =319.
3.19 101 = 3.19 10 =31.9
312 CHAPTER 5 Exponents and Polynomials
OBJECTIVES OBJECTIVE 1 Express numbers in scientific notation. Numbers occurring in
science are often extremely large (such as the distance from Earth to the sun,
93,000,000 mi) or extremely small (the wavelength of yellow-green light, approxi-
mately 0.0000006 m). Because of the difficulty of working with many zeros, scientists
often express such numbers with exponents, using a form called scientific notation.
An Application of Exponents: Scientific Notation
5.3
1 Express numbers in
scientific notation.
2 Convert numbers in
scientific notation
to numbers without
exponents.
3 Use scientific
notation in
calculations.Scientific NotationA number is written in scientific notationwhen it is expressed in the form
a: 10 n, where and 1 ...|a| 610 nis an integer.
It is not necessary
to write 2.0.Writing a Number in Scientific Notation
Step 1 Move the decimal point to the right of the first nonzero digit.
Step 2 Count the number of places you moved the decimal point.
Step 3 The number of places in Step 2 is the absolute value of the exponent
on 10.
Step 4 The exponent on 10 is positive if the original number is greater than
the number in Step 1. The exponent is negative if the original num-
ber is less than the number in Step 1. If the decimal point is not
moved, the exponent is 0.http://www.ebook777.com
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