Dimensional Analysis - Mounds View School Websites
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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
#1abc, 2abc, 3ab, 4abc, 5ac