Dimensional analysis notes
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Dimensional Analysis
Dimensional Analysis
Dimensional analysis: a method
of solving problems that involves
using equivalence statements
and conversion factors; the units
(dimensions) guide you through
the problem
Dimensional Analysis
Equivalence statement: an
accepted relationship between
two units
Example: 12 inches = I foot
Dimensional Analysis
Conversion factors: two possible ratios from an
equivalence statement
Equivalence statement: 12 inches = I foot
Conversion factors:
12 inches
I foot
and
I foot
12 inches
Dimensional Analysis
Look at the equivalence statements on page 163.
Write down the the two possible conversion factors for each
equivalence statement.
How to use dimensional analysis
Steps:
1. Identify starting & ending units.
2. Line up conversion factors so units cancel.
3. Multiply all top numbers & divide by each bottom
number.
4. Check units & answer.
Dimensional Analysis
Example problems using the equivalence statements on
page 163. Be sure to copy the work done on the board.
Example #1: 62 cm = ____ in
Example #2: _____ yd = 2.45 m
Dimensional Analysis
You will need to match the metric prefixes you
memorized to units and construct your own
equivalence statements.
Example: kilo is 103
Which is true for the prefix kilo matched to the unit
meter (m)?
1 m = 103 km or 103 m = 1 km
Dimensional Analysis
Which is true for the prefix kilo?
1 m = 103 km or 103 m = 1 km
Remember: the “1” always goes with the prefix; the
“meaning” you memorized always goes with the unit
(without the prefix).
Which one above is correct?
Dimensional Analysis
Write an equivalence statement by matching the unit g
(gram) to these prefixes: M, d, c, µ.
Dimensional Analysis
Use dimensional analysis to solve these problems. Be
sure to show all work.
a. 3.45 cm = ___ m
b.
2.4 X 10-3 g = ___ng
c.
6.8 X 105 ms = ___ s
Dimensional Analysis
Use the equivalence statements on page 163 to do
problems 39 and 40 on page 166.
One equivalence statement needed that is not listed on
page 163:
16 oz = 1 lb