Texts: Chapter 2b I Appendix
SKILL 1: Identifying Measurements and Conversion Factors
Dimensional analysis is all about changing the units of your measurement using a series of conversion factors. A measurement is a number associated with a single unit, such as 284 feet, 5 miles, or 21 gallons. Conversion factors are numerical relationships between units, such as "There are 12 inches in a foot" (12 in/1 ft) or "My car gets 35 miles per gallon" (35 mi/gal). Most often, dimensional analysis problems should begin with the measurement and subsequently apply conversion factors until the desired units are achieved. Therefore, it is important to be able to distinguish between measurements and conversion factors.
CIRCLE measurement or conversion. For each conversion factor, write factor for each value. Write it as a ratio of the two units.
Measurement: 60 ml
Conversion factor: 1 hr
Measurement: I drove 60 mph.
Conversion factor: 1 hr
Measurement: My cat weighs 2 kg.
Conversion factor: 1 kg
Measurement: There are 100 years in a century.
Conversion factor: 1 century
Measurement: A meter is equivalent to 100 cm.
Conversion factor: 100 cm
Measurement: The stick is 100 cm in length.
Conversion factor: 1 stick
Measurement: One inch is 2.54 cm.
Conversion factor: 2.54 cm
Conversion factors can be given in the problem or you will know them from experience. Metric conversion factors are used so often that it would be wise to commit them to memory. See if you can relate the metric prefix to its value. Fill in either the value or a metric prefix. Reference this table for assistance. Switch out prefix for value. Switch out value for prefix.
1 km = 1000 m
10 s = 1 s
10^6 mega (M)
10^3 kilo (k)
base unit
10^-1 deci (d)
10^-2 centi (c)
10^-3 milli (m)
10^-6 micro (Ī¼)
10^-9 nano (n)
10^-12 pico (p)
1 g = 100 cg
10 g = 1 g
1 mmol = 10 mol
1 K = 1 K
10 m = 1 m
1 nm = 10 nm