1. Scientific Notation Chapter 4 Section 3
MTH Algebra
Scientific Notation
Chapter 4 Section 3

2. 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.

3. 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
= 1.0 x 10-7

4. 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

5. Express in Scientific Notation
Example: x 10-5
Example:
1,340,000
1.34 x 106

6. 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

7. Express in Decimal Form (without exponents)
Example: x 1010
3.201 x 10,000,000,000
Move 10 places to the right
32,010,000,000
Example: 5.23 x x 1/100 Move 2 place to the left

8. 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

9. 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 move three places to the left
0.076 meters

10. Scientific Notation with a Coefficient of 1
Example:
Write Kilometers without the metric prefix.
472.1 x move three places to the right
472,100 meters
Write 12.5 nanometers without the metric prefix.
12.5 x move three places to the left
meters

11. 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

12. Calculation using Scientific Notation
Example: Divide and write in Scientific Notation.

13. Calculation using Scientific Notation
Example: The weight of the Earth is x 1024 kg. The weight of the Earth’s Moon is 7.35 x 1022 kg
How much greater is the weight of the Earth than the weight of its Moon?
How many times greater is the weight of the Earth than the weight of its moon? A. B.

14. 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

15. HOMEWORK 4.3
Page 257 #17, 18, 21, 31, 35, 65, 69, 72