Dimensional
Analysis
Unit 1.3
Chapter 1 Section 2
What is dimensional analysis?
A tool for converting from one unit to another
Equality = the quantity of two different units that
represent equal amounts
Ex. 1 dollar = 4 quarters
Important equalities to remember:
1 kilo-____ = 1000 base units (base units = g, l, m)
1 base unit = 1000 milli
1 mL = 1 cm3
Rules for Dimensional Analysis
1.
2.
3.
4.
5.
Grams
ALL Numbers are written as fractions
Write everything WITH its unit (NO NAKED
numbers)
Arrange conversion factors so the
previous unit cancels (diagonal units)
Numbers on TOP are MULTIPLIED
Numbers on BOTTOM are DIVIDED
Liters
Conversion Factor
To convert from one unit to another you
need an equality
When you write an equality as a fraction it
is called a conversion factor
Conversion Setup
Done properly the old units cancel out giving you
the amount in the new units
Practice Proper Setup
What are four equalities for time?
1 min = _______ seconds
1 hour = ______ min
I day = _______ hours
1 year = ______ months
Practice Proper Setup
Convert 9 hours into seconds using
equalities
Practice
If John has 12 shillings, how many dollars is that
worth if 1 shilling equals 2 yen, 6 yen equal 3 franks
and 2 franks equal 4 dollars?
Practice
If you have 9 g of a substance that has a density
of 3g/mL, what is the volume of the substance in
milliliters?
Practice
A corvette can travel 17.0 miles on one gallon of
gasoline. How many kilometers per liter is this?
(1.61 km = 1 mile; 1 Liter = 0.264 gallon)