Download Scientific Notation

MTH 10905
Algebra
SCIENTIFIC NOTATION
CHAPTER 4 SECTION 3
Convert Numbers to and from Scientific
Notation
Numbers written in Scientific notation
is written as a number greater than or
equal to 1 and less than 10,
(1 < 10), Multiplied by a power of
10.
Convert Numbers to and from Scientific
Notation
Examples of numbers
in scientific notation
6000 = 6 x 103
6,160,000,000 = 6.16 x 109
0.0000001 = 1.0 x 10-7
To Write a Number
in Scientific Notation
 Move the decimal point in the right of the first nonzero
digit. ≥1 and <10
 Count the number of decimal places you moved the
original number.
If the original number is 10 or greater then count is
positive.
If the original number is <1 then count is negative.
 Multiple step 1 by 10 to the power of your count in step 2
Express in Scientific Notation
Example:
Example:
0.0000786
1,340,000
7.86 x 10-5
1.34 x 106
Convert a Number from Scientific Notation to
Decimal Form
 Observe the exponent in the power of 10
 If exponent is positive ≥1 and <10 move the
decimal to the right. May have to add zero’s
 If exponent is 0. Drop the factor 100 because that
equals 1. Do NOT move the decimal.
 If exponent is negative <1 move decimal to the
left. May have to add decimals
Express in Decimal Form
(without exponents)
Example:
3.201 x 1010
3.201 x 10,000,000,000
Move 10 places to the right
32,010,000,000
Example:
5.23 x 10-2
5.23 x 1/100
Move 2 place to the left
0.0523
Scientific Notation with a Coefficient of 1
 The metric system is used in every westernized nation
except the United States
 kilograms, milligrams, gigabytes
 1 millimeter (m) = 10-3 or 1/1000
1 megagram (M) = 106 or 1,000,000
 See other in table on page 253
Scientific Notation with a Coefficient of 1
 Remember that we assume 1 when no numerical
coefficient exists
 Example:
Write 76 millimeter without the metric prefix.
76 x 10-3 move three places to the left
0.076 meters
Scientific Notation with a Coefficient of 1
 Example:
Write 472.1 Kilometers without the metric
prefix.
472.1 x 103 move three places to the right
472,100 meters
 Example:
Write 12.5 nanometers without the metric
prefix.
12.5 x 10-9 move three places to the left
0.0000000125 meters
Calculation using Scientific Notation
 Use the rules of exponents
 Example: Multiply and write in decimal form.
(2.8 x 107)(3.0 x 10-3)
(2.8)(3.0)(107)(10-3)
8.4 x 107+(-3)
8.4 x 104
Move the decimal place 4 places to the right
84,000
Calculation using Scientific Notation
 Example: Divide and write in Scientific Notation.
5.6  103  5.6   10 3 
( 3)  ( 7 )
4


2
.
0

10

2
.
0

10


 
7
 2.8  107 
2.8  10
Calculation using Scientific Notation
 Example:
The weight of the Earth is 5.972 x 1024 kg. The
weight of the Earth’s Moon is 7.35 x 1022 kg
A. How much greater is the weight of the Earth than the weight
of its Moon?
B. How many times greater is the weight of the Earth than the
weight of its moon?
A.
597.20  1022

7.35  1022
589.85  1022
B.
5.972  10 24 5.972 10 24

 22
22
7.35  10
7.35 10
 .812517  10 24 22
Move the decimal back to the left 2
 .812517  10 2
Move the exponent back to 24
 .812517  100
5.8985  1024 kg
 81.25 times greater
Remember
 The numerical value preceding the base must be
greater than or equal to 1 but less than 10
 The sign of the exponent on the base indicates which
direction to move the decimal point.


Negative moves left
Positive moves right
HOMEWORK 4.3
Page 257
#17, 18, 21, 31, 35, 65, 69, 72