+

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