1. + Math Skills

2. + 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 Example: Convert 20 mi/hr to m/s

3. + Step 1: Write given with horizontal lines

4. + 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

5. + 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.

6. + Step 3: Multiply so units cancel out

7. + 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*10 3 = 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*10 3 Ex: 0.00351 = 3.51*10 -3

8. + 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*10 4 ) * (3*10 2 ) = 18 * 10 6 = 1.8 * 10 7 (6*10 8 ) / (3*10 2 ) = 2 * 10 6  10 6 NOT 10 4 (6*10 8 ) / (3*10 -2 ) = 2 * 10 8 -- -2 = 2 * 10 10

9. + Metric Prefixes YOU MUST MEMORIZE KILO, CENTI, and MILLI : MultiplePrefixAbbreviation 10 9 GigaG 10 6 MegaM 10 3 Kilok 10 -2 Centic 10 -3 Millim 10 -6 Microµ 10 -9 Nanon

10. + Metric Conversions 2.8 km = 2.8 * 10 3 m = 2800 m 17.1 mL = 17.1 * 10 -3 L = 0.0171 L Convert 50 m to km Convert 15 mg to kg