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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 £ a < 10), Multiplied by a power of 10.
Convert Numbers to and from Scientific Notation
6000 = 6 x 103
6,160,000,000 = 6.16 x 109
0.0000001 = 1.0 x 10-7
Examples of numbers
in scientific notation
To Write a Numberin 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
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: 5.23 x 10-2
5.23 x 1/100Move 2 place to the left0.0523
Example: 3.201 x 1010
3.201 x 10,000,000,000Move 10 places to the
right32,010,000,000
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 1/10001 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 left0.076 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 right472,100 meters
Example:Write 12.5 nanometers without the metric prefix.
12.5 x 10-9 move three places to the left0.0000000125 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 right84,000
Calculation using Scientific Notation
Example: Divide and write in Scientific Notation.
4)7()3(7
3
7
3
10 0.210 0.210
10
8.2
6.5
10 8.2
10 6.5
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 kgA. 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?
22
22
22
24
597.20 10
7.35 10
589.85 10
Move the decimal back to the left 2
Move the exponent back to 24
5.8985 10 kg
greater times25.81
100 812517.
10 812517.
10 812517.
10
10
35.7
972.5
10 35.7
10 972.5
2
2224
22
24
22
24
A. B.
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