DIMENSIONAL ANALYSIS
Chapter 5,
Section 3A
LET’S REVIEW THE METRIC SYSTEM
In General:
 Kilo = 1000 of base
 Deci = 0.1 of base
 Centi = 0.01 of base
 Milli = 0.001 of base
Example:
 Kilometer = 1000 m
 Meter = base unit
 Decimeter = 0.1 m
 Centimeter = 0.01 m
 Millimeter = 0.001 m
CONVERTING UNITS OF MEASUREMENT
 You convert units of measurement in your everyday life.
 How would you convert from minutes to seconds?
 1 minute = 60 seconds
 Doing unit conversions in chemistry is no dif ferent, we just
call it dimensional analysis.
 Hint: Unit conversions are exact numbers, so the only sig figs
you count are the ones in your original number
 In chemistry, we use conversion factors, a ratio used to
convert from unit to another.
 I will give you non-metric conversion factors. Ex grams to pounds
 As a conversion factor, minutes to seconds would be written
like this:
60 seconds
1 minute
STEPS FOR CONVERTING UNITS
1. Identify the unit you are starting in, and
identify the unit you need to convert to.
2. Choose the appropriate conversion factor(s)
to get from your starting unit to your ending
unit.
3. Set-up your problem, so your units are easily
compared and canceled
4. Multiply the top, multiply the bottom, divide
the top by the bottom
MINUTES TO SECONDS
How many seconds are in 5 minutes?
1. Starting units: minutes, ending units: seconds
2. Conversion factor: 60 seconds/ 1 minute
3. Set-up:
5 minute
60 seconds
1 minute
4. Multiply top: 5 x 60 = 300, Multiply bottom: 1 , Divide top by
bottom: 300/1 = 300 seconds, this answer already has the
correct number of sig figs
METRIC CONVERSIONS
How many meters are in 300 centimeters?
1. Starting units: centimeters, Ending units: meters
2. Conversion factor: 0.01 m = 1 cm, or 100 cm = 1 m
3. Set-up:
300 centimeter
1 meter
100 centimeter
4. Multiply top: 300 x 1 = 300, Multiply bottom: 100, Divide
top by bottom: 300/100= 3 meters, this answer already has
the correct number of sig figs
2 CONVERSION PROBLEMS
 For some dimensional analysis problems you will have to use
2 conversion factors to get to an answer. But you still use the
same steps! Let’s look at an example:
 How many seconds are in 4 hours?
1. Starting units: hours, Ending units: seconds
2. Conversion factors: 60 minutes = 1 hour, 60 seconds = 1
minute
3. Set-up:
4.0 hours
60 minutes 60 seconds
1 hour
1 minute
4. Multiply the top: 4 x 60 x 60 = 14400, Multiply the bottom:
1 x 1 = 1 , Divide top by bottom: 14400/1 = 14400 seconds,
sig fig answer 14000 seconds
2 CONVERSION PROBLEMS
How many yards are in 250 centimeters? Hint: 1 m = 1 .094 yds
1. Starting units: centimeters, Ending units: yards
2. Conversion Factors: 100 cm = 1 m, 1 m = 1 .094 yds
3. Set-up:
250.0 cm
1m
1.094 yds
100 cm
1m
4. Multiply the top: 250 x 1 x 1 .094 = 273.5, Multiply the
bottom: 100 x 1 = 100, Divide the top by the bottom:
273.5/100 = 2.735 yards, this answer already has the
correct number of sig figs
PRACTICE TIME!
 Try practicing dimensional analysis on your own on the
worksheet. This worksheet will be a part of your homework
packet.
MULTI-STEP CONVERSION PROBLEMS
 Many dimensional analysis problems will have more than 2
conversions. However, you follow the same steps
The length of a marathon is 26.2 mi. What is this distance in
kilometers? Hint: 1 mi = 1760 yds, 1 m = 1 .094 yd
1. Starting units: miles, Ending unit: kilometers
2. Conversion factors: 1 mi = 1760 yds, 1 m = 1 .094 yd, 1 km=
1000 m
3. Set-up: 26.2 mi
1760 yd
1m
1 km
1 mi
1.094 yd
1000 m
4. Multiply top: 26.2 mi x 1760 yd x 1 m x 1 km = 46112,
Multiply bottom: 1 mi x 1 .094 yd x 1000 m = 1094, Divide
top by bottom: 46112/1094 = 42.1 km (correct sig figs)
MULTI-STEP CONVERSION
How many seconds are in 25 days?
1. Starting unit: days, Ending unit: seconds
2. Conversion factors: 1 day = 24 hrs, 1 hr = 60 min, 1 min =
60 sec
3. Set-up:
25 days
24 hrs
60 min
60 sec
1 day
1 hour
1 min
4. Multiply the top: 25 x 24 x 60 x 60 = 2160000, Multiply the
bottom: 1 x 1 x 1 = 1 , Divide top by the bottom: 2160000/1
= 2160000 seconds, sig fig answer: 2200000
WHAT ABOUT MEASUREMENTS WITH 2
UNITS?
 Some measurements, like density (g/mL), have two units. You
can still use dimensional analysis to convert one or both of
the units present.
 You will still use the same steps, but your set -up will be longer
and you have to be more careful about canceling your units.
 For your conversion factors, I recommend separating them
into the units you need to use for the top unit and the bottom
unit
 Let’s look at a few examples
2 UNIT CONVERSIONS
Race cars routinely travel at an average speed of 225 mi/hr.
What is the speed in km/ hr? Hint: 1 mi = 1760 yd, 1 m = 1 .094
yd
1. Starting units: mi/hr, Ending units: km/hr, Note: hours is the
same in both
2. Conversion factors: 1 mi = 1760 yd, 1 m = 1 .094 yd, 1000 m
= 1 km
3. Set-up:
225 mi
1760 yd
1m
1 km
hr
1 mi
1.094 yd
1000 m
4. Multiply top: 26.2 mi x 1760 yd x 1 m x 1 km = 46112,
Multiply bottom: 1 mi x 1 .094 yd x 1000 m = 1094, Divide
top by bottom: 46112/1094 = 42.1 km/ hr (correct sig figs)
2 UNIT CONVERSIONS
Silver has a density of 10.5 g/cm3; what is the density of silver
in kg/L?
1. Starting units: g/cm3, Ending units: kg/L, Note: you have to
convert both units
2. Conversion factors: Top unit: 1000 g = 1 kg, Bottom unit: 1
cm3 = 1 mL, 1000 mL = 1 L
3. Set-up: 10.5 g
1 kg
1 cm3
1000 mL
cm3
1000 g
1 mL
1L
4. Multiply the top: 10.5 x 1 x 1 x 1000 = 10500, Multiply the
bottom: 1 x 1000 x 1 x 1= 1000, Divide top by the bottom:
10500/1000= 10.5 kg/L.
2 UNIT CONVERSIONS
You are driving at 50 mi/ hr; how fast are you going in m/s? Hint:
1 mi = 1760 yd, 1 m = 1 .094 yds
1. Starting units: mi/hr, Ending units: m/s
2. Conversion Factors: Top unit: 1 mi = 1760 yd, 1 m = 1 .094 yd,
Bottom unit: 1 hr = 60 min, 1 min = 60 s
3. Set-up:
50 mi
1760 yd
1m
1 hr
1 min
hr
1 mi
1.094 yd
60 min
60 sec
4. Multiply the top: 50 x 1760 x 1 x 1 x 1= 88000, Multiply the
bottom: 1 x 1 .094 x 60 x 60= 3938.4, Divide the top by the
bottom: 88000/3938.4= 22 m/s
LET’S PRACTICE
 This worksheet is great practice for the skills we learned
today and yesterday.
 Use this worksheet to gauge your understanding of
dimensional analysis
 This worksheet will be a part of your homework packet due on
the day of the test.