1. Prefixes, Conversion Factors, and the Factor Label Method
Chapter One

2. Commonly Used Prefixes
Power 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 Notation
Certain 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 seconds
1 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 Method
Decide 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: $10
Conversion 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 miles
10.1mi = 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