Dimensional Analysis
What is dimensional analysis?!
 A way
to analyze and solve problems
using the units, or dimensions, of the
measurements
 Also
known as conversion factors
Problem: How many seconds do
students spend at school everyday?
 Knowns:



School starts at 7:25am and ends at 2:05pm,
a total of 7.67 hours
1 hour = 60 minutes
1 minutes = 60 seconds
 Unknown:

How many seconds are in a school day?
Solution:
7 . 67 h 
60 min
1hour

60 s
1 min
 27 , 612 s
Practice Problems:
1. How many minutes are there in 1 week?
1week 
7 days
1week

24 hours
1day

60 min
1hour
 10 , 080 min
Practice Problems
2.
How many seconds are there in a year?
1 year 
365 days
1 year

24 h
1day

60 min
1h

60 s
1 min
 3 . 1536  10
7
Using Dimensional Analysis to
Solve Problems

You are cooking Thanksgiving dinner. You have a
recipe that makes 6 pounds of stuffing. From previous
Thanksgivings you noticed that an average person eats
0.452 pounds. How many people can you invite to your
Thanksgiving dinner this year?
6 pounds 
1 guest
0 . 452 pounds
 13 guests
Practice Problems
1.
An experiment requires that each student use an 8.5-cm length of
magnesium ribbon. How many students can do the experiment if
there is a 570-cm length of Mg ribbon available?
570 cm 
1 student
8 . 5 cm
 67 students
Practice Problem
2. A 1.00-degree increase on the Celsius scale is equivalent to a
1.80-degree increase on the Fahrenheit scale. If a temperature
increases by 48.0 Celsius, what is the corresponding
temperature increase on the Fahrenheit scale?
48 Celsius 
1 . 80 F
1 . 00 Celsius
 86 . 4 F
Converting Between Units

Suppose that a laboratory experiment requires 7.5 dg of
magnesium metal, and 100 students will do the experiment. How
many grams of magnesium should your teacher have on hand?
Multiplying 100 students by 7.5 dg/student gives you 750 dg. But
then you must convert dg to grams.
750 dg 
1g
10 dg
 75 g
Practice Problems
Convert the following using dimensional
analysis
1.
a.
0.044 km to meters (1000 m = 1 km)
b.
4.6 mg to grams (1000 mg = 1 g)
c.
0.107 g to centigrams (100 centigrams= 1 g)
Multistep Unit Conversion
What is 0.073 cm in micrometers?
Knowns:
length = 0.073 cm = 7.3 x 10-2
102 = 1 m
1 m = 106 micrometers
Unknowns:
length in micrometers
7 . 3  10
2
cm 
1m
2
10 cm
10  m
6

1
m
 7 . 3  10  m
2
Practice Problem

The radius of a potassium atom is 0.227 nm. Express this radius in
the unit centimeters.
0 . 227 nm 
1m
9
10 nm

100 cm
1m
 2 . 27  10
8
cm
Homework!!!
 p.R68
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