Dimensional Analysis
1 Place "given " in upper left corner
2 Label diagonal identical - Upper Left to Lower Right
3 Determine what conversion you will use:
4 If you are converting to metric units, always match the Conversion Factor with the Base
Unit
5 Repeat steps 2 & 3 and add conversion columns until upper right box has the same label
you want in your answer
6 Multiply all numbers on top and divide by all numbers on the bottom
Convert to Scientific Notation at this time to complete your conversion
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Example:
250 kg = ______mg
Given
250 kg = ______mg
What you want
250 kg = ______mg
Conversion Units= “k” & “m”
Conversion Factor (from metric chart)
k = kilo = 1x103
Base Unit = “g” (grams)
m = milli = 1x10-3
Sample Conversion
250kg
1x103g
1mg
250 x103
250 x 106 = 2.50 x 108 mg
1 kg
1x10-3 g
1 x 10-3
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1. mm to pm
2. nanometers to Megameters
3. kg to g
4. mm to kg
Scientific Notation
1. Move the decimal so that you have only 1 number to the left of the decimal.
2. Count how many times you moved the decimal.
3. The number of times you moved the decimal becomes the exponent of the power of
10.
4. If the original number was larger than any number in the “ones” position, your
exponent is Positive
5. If the original number was a decimal, your exponent is negative.
Example: 2,300 = 2.3x103
Convert to Scientific Notation:
1. 1,450,0000 ______________
2. .00302
______________
3. 12.2
______________
4. 186,000
______________
5. 70,000,000 ______________
Convert to standard notation:
1. 1.2 x 104 ______________
2. 2.67 x 10-5 _____________
3. 3.2 x 108 ______________
4. 6.25 x 10-6 _____________
.0023=2.3x10-3
Multiplying and Dividing Exponents
When you multiply an exponent in scientific notation you add.
Example: 1x105 times 1x106 = 1x1011
When you divide an exponent in scientific notation you:
1. Switch the symbol of the exponent in the denominator (bottom number) and cancel.
2. “Combine” the switched exponent with the exponent in the numerator (top)
Example: 1x105 / 1x102 =1x105-2 = 1x103
- When you see division on a test the divide sign is /
- The second power of ten is the one you switch signs.
- In example - 102 switches to 10-2
- The -2 is “combined” with the exponent of the first power of 10, which is 5
- The result is 5-2=3
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Multiplying and Dividing Scientific Notation
1. Mentally multiply or divide the numbers before the power of 10 and write your answer
2. Multiply or divide the powers of 10 as described above and write your answer.
a. (15x1012 in Multiplication example and .5x1010 in Division example)
3. Look at your result and convert, if necessary to proper scientific notation. (See Example)
4. Whenever you make your number smaller in your final conversion, (15 to 1.5 in multiplication
example) you make your exponent bigger by the exact same number of times you moved the decimal.
If you make your final number bigger, the exponent will get smaller. (Division example)
Example:
Multiplication: 3 x 105 times 5 x 107 = 15 x 1012 = 1.5 x 1013
Division: 2.5 x 104 / 5 x 10-6 = .5 x 1010 =5 x109
1. 6 x 1020 x 3 x 10-15 _____________________
2. 2 x 105 x 3 x 10-10 _____________________
3. 3.0 x 10-12 x 4.0 x 108 __________________
4. 6.2 x 105 / 2 x 103 ____________________
5. 3.0 x 106 / 6 x 10-16 ___________________