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