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