1 Prefixes, Conversion Factors, and the Factor Label MethodChapter One

2 Commonly Used PrefixesPower Prefix Abbreviation nano n micro µ milli m centi c deci d 101 deka da 103 kilo k 106 Mega M 109 Giga G

3 Relation to Scientific NotationCertain prefixes are used to represent specific powers of 10. For example: 1000 can be written as 1 x 103 103 is represented by the prefix “kilo” so… 1000m becomes 1 km

4 Conversion Chart (shown for meters, but can be used for any unit)1 m = 1,000,000,000 nm 1 m = 1,000,000 µm 1 m = 1,000 mm (or 1mm = 1/1000 m) 1 m = 100 cm (or 1cm = 1/100 m) 1 m = 10 dm 1 dam = 10 m 1 km = 1,000 m 1 Mm = 1,000,000 m 1 Gm = 1,000,000,000m

5 Conversion Factors Examples 1 hour = 60 mins 1 min = 60 seconds1 ft = 12 inches 1 mile = 5280 feet 1 kg = 1,000 g

6 Factor Label Method This is used to convert from one unit to another, or even in converting derived units. Even though the number changes, the QUANTITY does not! (like converting currency – you do not get gain or lose money)

7 Conversions Using Factor Label MethodDecide what is being asked Write down what is given Find the conversion factors Set up problem and crunch numbers

8 Conversion factors equal 1 The top must be equal to the bottom Units you want to cancel must be on opposite sides of the division line 3.0ft x 12in = 36 in ft 3.0ft x 1ft = 0.25 ft2 in in

9 Example 1: Gas costs $1.45 per gallon. You have $10. How many gallons of gas can you get?

10 Given: $10 Conversion Factor: 1 gal = $1.45 $10 1 1 gal $1.45 x = 6.90 gal

11 Example 2: Gas costs $1.45 per gallon. You have $10. Your car gets 44.2 miles per gallon. How many miles can you drive on a $10 fill-up?

12 $10 1 1 gal $1.45 44.2 mi 1 gal x x =305 mi Given: $10Conversion Factor: 1 gal = $1.45 1 gal = 44.2 miles $10 1 1 gal $1.45 44.2 mi 1 gal x x =305 mi

13 Example 3: Gas costs $1.45 per gallon. You have $10. Your car gets 44.2 miles per gallon. You drive an average of 10.1 miles per day. How many weeks will you be able to drive before getting gas again?

14 x Given: $10 Conversion Factor: 1 gal = $1.45 1 gal = 44.2 miles10.1mi = 1 day 1 week = 7 days $10 1 1 gal $1.45 44.2 mi 1 gal 1 day 10.1 mi 1 wk 7 days = 4.31wks x x x x

15 Factor Label Examples

16 23,000 µm mm 14 km cm 72 mm cm 6 mi in 8 days sec 19 kg mg 15 ft / sec mi / hr 92 m / sec km / day 42 ft / hr mi / sec

17 Factor Label Example Answers

18 Number 1

19 Number 2

20 Number 3

21 Number 4

22 Number 5

23 Number 6

24 Number 7

25 Number 8

26 Number 9