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Math Skills
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Fence Posting
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Used to convert units
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Ex. Km/s to mi/hr
Rules:
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Use horizontal lines, not slashes for division to avoid confusion
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Find a conversion factor
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Multiply so units cancel out
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Cross out units as you go
Video Examples:
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https://www.youtube.com/watch?v=q7Rq1FrevY4&feature=youtu.be
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http://www.youtube.com/watch?v=-oyM_hvkzqo&feature=youtu.be
Example: Convert 20 mi/hr to m/s
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Step 1: Write given with horizontal
lines
20mi
hr
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Step 2: Find a conversion factor
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We can’t directly convert from miles to meters, but we can
convert from miles to feet, feet to inches, inches to
centimeters, and finally centimeters to meters.
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1 mi = 5280 feet
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1 in = 2.54 cm
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Continued
Let’s convert miles to feet:
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20mi
hr
The conversion factor is 1 mi = 5280 ft
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We want to multiply so that the miles cancels out, like this:
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20mi 5280 ft
x
hr
1mi
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Notice that with miles on both the numerator and
denominator, it cancels out.
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Now we have ft/hr. We will convert feet to meters in several
steps, and then hours to seconds.
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Step 3: Multiply so units cancel out
20mi 5280 ft 12in 2.54cm
1m
1hr
8.9m
x
x
x
x
x
=
hr
1mi
1 ft
1in
100cm 3600s
s
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Scientific Notation
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To convert from scientific notation to decimals:
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If the exponent is positive, move the decimal that many places to
the right.
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If the exponent is negative, move the decimal that many places to
the left.
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Ex: 5.4*103 = 5400
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Ex: 5.2*10-3 = 0.0052
To convert from decimals to scientific notation
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Move the decimal such that number ranges between 0-10
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The number of places you moved the decimal becomes the
exponent
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Ex: 2730 = 2.73*103
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Ex: 0.00351 = 3.51*10-3
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Math with Scientific Notation
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Multiplication:
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Add the exponents
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Perform the mathematical operation to the base numbers
Division:
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Subtract the exponents
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Perform the mathematical operation to the base numbers
Examples:
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(6*104) * (3*102) = 18 * 106 = 1.8 * 107
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(6*108) / (3*102) = 2 * 106  106 NOT 104
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(6*108) / (3*10-2) = 2 * 108 -- -2 = 2 * 1010
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Metric Prefixes
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YOU MUST MEMORIZE KILO, CENTI, and MILLI :
Multiple
Prefix
Abbreviation
109
Giga
G
106
Mega
M
103
Kilo
k
10-2
Centi
c
10-3
Milli
m
10-6
Micro
µ
10-9
Nano
n
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Metric Conversions
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2.8 km = 2.8 * 103 m = 2800 m
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17.1 mL = 17.1 * 10-3 L = 0.0171 L
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Convert 50 m to km
50m 1km
x
= 0.050km
1 1000m
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Convert 15 mg to kg
15mg 1*10-3 g 1kg
x
x
=15*10-6 kg =1.5*10-5 kg
1
1mg
1000g