Dimensional Analysis and
Metric Conversions
SC Standards
PS-1.5
Organize and interpret the data
from a controlled scientific
investigation by using mathematics
(including formulas and dimensional
analysis), graphs, models, and/or
technology.
Dimensional Analysis
Conversion factors:
•using ratios of equivalent values to
convert from one unit of measure to
another.
1 gram = 1000 milligrams
1g
1000 mg
or
1000 mg
1g
60 sec = 1 min.
60 sec
1 min.
or
1 min.
60 sec
What would the conversion factors
be for years and days?
365 days
1 year
or
1 year
365 days
Dimensional Analysis
1.) Write down given number and unit
2.) Write down “x” and a line
3.) Put given unit on side of line so it will
cancel and the desired unit on the other
side (may take more than 1 step)
4.) Fill in appropriate numerical relationship
for the ratio
5.) Multiply the top and divide by the
bottom
…see examples…
• Example #1
–How many minutes are there
in 1 year?
1 year x _______
365 days x ____
24 hr x _____
60 min.
1 year
1 day
1 hr
= 525,600 minutes!!
Example #2 - How many inches are
there in 85.6 cm? (1in = 25.4mm)
10 mm x _____
1 in
85.6cm x _____
1 cm
25.4 mm
= 33.7 in.
Example #3 - How many fluid ounces
are there in 2.0 gallons?
(1gall = 4 qts, 1 qt = 2 pints, 1 pint = 2 cups,
1 cup = 8 fl. oz.)
4 qts x _____
2 pt
x _____
1 gal
1 qt.
2 cup x _____
x _____
8 fl. oz.
1 pt.
1 cup
= 256 fl. oz.
2.0 gall
Unit Check
1.4 day
x 1 day
24 hr
Units = day2/hr2
x
60 min
1 hr
x 60 sec
1 min
Not the final unit needed
LecturePLUS Timberlake
11
Learning Check
If your pace on a treadmill is 65 meters per
minute, how many seconds will it take for you to
walk a distance of 8450 feet?
LecturePLUS Timberlake
12
Solution
Initial
8450 ft
x 12 in.
1 ft
x 1 min
65 m
x 2.54 cm
1 in.
x 1m
100 cm
x 60 sec = 2400 sec
1 min
final (2 SF)
LecturePLUS Timberlake
13
Compare using <, >, or =.
25) 63 cm
26) 536 cm
6m
53.6 dm
27) 5 g
28) 43 mg
508 mg
5g
29) 1,500 mL
30) 3.6 m
1.5 L
36 cm