dimensional analysis dhs chemistry ferrer. setting up ratios 100 centimeters = 1 meter can be...
TRANSCRIPT
Dimensional Analysis
DHS Chemistryferrer
Setting Up Ratios100 centimeters = 1 meter can be
written as 100 cm OR 1 m___ 1 m 100 cm
8 slices = 1 pizza can be written as 1 pizza OR 8 slices___ 8 slices 1 pizza
The Format # x # x # x # = 1 # # #
OR# # # = 1 # #
Note: Unless you are using 1 as a spot filler, all numbers should ALWAYS include units
Understanding order of operations & typing in
calculator keys correctlySolve. 10 13 6 =
2 4
Method 1: 10 X 13 X 6 = 780 then divide 97. 5 2 x 4 = 8
Method 2: 10 X 13 X 6 / 2 / 4 = 97.5 130 780 390 97.5
Method 3: 10 X 13 / 2 X 6 / 4 = 97.5 130 65 390 97.5
Try It
15 2 3 1.2 4 = 1 4 5 14 5
0.308
Canceling out unitsJust as numbers are multiplied and
divided, units are too. Cancel out all units that are located in both the numerator and denominator to reveal the left over units.
cm in feet yard = yard
cm in feet
Try It
week day hr min sec = sec
1 week day hr min
Putting the numbers & units together
3 weeks 7 day 24 hr 60 min 60 sec = 1 1 week 1 day 1 hr 1 min
=1814400 sec
Rules?
I. One-Step Conversions
282.3 pizzas
I. One- Step ConversionsEX 1: Determine the number of slices in 282.3
pizzas Step 1) what are you given? Step 2) What are you trying to get?
Step 3) List your relationships (remember from pg 1 of the
notes)
Step 4) Set up your problem8 slices
slices1 pizza
=2258.41
282.3 pizzas
Number of slices
1 pizza = 8 slices
Dozen of eggs
1 dozen
EX 2: Determine the number of dozen eggs in 3.8 x 103 eggs.
Step 1) what are you given? 3.8 X 103 eggsStep 2) What are you trying to get? Dozen eggs
Step 3) List your relationships12 eggs = 1 dozen
Step 4) Set up your problem
3.8 X 103 eggs 12
eggs
=3171
The
se s
houl
d m
atch
Practice1. Determine the number of feet in 2821
inches. want given
2821 in
1 foot feet12 in
= 2351
Relationship1 foot = 12 inches
Start with what’s given
Practice2. Determine the number of g in 0.03455
kgwant given
0.03455 kg
1000 g g1 kg
= 34.61
Relationship1000g = 1kg
Start with what’s given
wantgiven
37 mi 1.6093 km km1 mi
= 59.51
Relationships1 mi = 1609.3 meter
1 mi = 1.6093 km Start with what’s given
99 mi 1.6093 km km1 mi
= 1591
Solving the same problem, but in a
different way
1 km
wantgiven
37 mi 1609.3 m km1 mi
= 59.51
Relationships1 mi = 1609.3 meter
1 km = 1000 m Start with what’s given
1000 m
For every problem, start with:
Given:
Want:
Relationships:
II. Multi-Step Conversions
Ex. 1 Convert 0.115 km to cm
Given:
Want:
Relationships:
0.115 km
____ cm
100 cm = 1 m
1 km = 1000 m
Ex. 1 Convert 0.115 km to cm
wantgiven
0.115 km 1000 m
cm
1 km
= 1.15 x 104
1
Relationships1km = 1000m
100cm = 1m
Start with what’s given
1 m
100 cm
Ex. 2 Convert 323 mL to cups
Given:
Want:
Relationships:
323 mL
____ cups
1000 mL = 1 L
1 L = 1.06 quarts
1 quart = 4 cups
1.06 qt.
Ex. 2 Convert 323 mL to cups
wantgiven
323 mL 1 L
cups
1000 mL
= 1.37
1
Relationships1000 mL = 1L
1L = 1.06 quarts
1 quart = 4 cups
Start with what’s given
1 L 1 qt.
4 cups
Practice 1: Convert 7.005 ft to mm
Given:
Want:
Relationships:
7.005 ft
____ mm
1 foot = 12 inches
1 inch = 2.54 cm
100cm = 1 m
1m = 1000mm
2.54 cm
Practice 1: Convert 7.005 ft to mm
wantgiven
7.005 ft12 in
mm
1 ft
= 2135
1
Relationships1 foot = 12 inches
2.54cm = 1 in
100 cm = 1 m
1 m = 1000 mmStart with what’s given
1 in 100 cm1 m 1000
mm1 m
Practice 2: calculate the number of seconds in 2 years
Given:
Want:
Relationships:
2 years
____ seconds
1 year = 365.25 days
24hrs = 1 day
60 min = 1 hr
1 min = 60 sec
24 hrs
Practice 2: calculate the number of seconds in 2 years
want given
2 years 365.25 days
seconds
1 year
= 6.31 X 10 7
1
Relationships1 year = 365.25 days
1 day = 24 hours
1 hr = 60 min
1 min = 60 secStart with what’s given
1 day 1 hr60 min
60 sec1 min
What does that price mean?
$1.99 = 1lb
III. Combination Unit Conversions
Writing Clean Fractions
Take the following quantities and turn it into a clean fraction as if you were starting a dimensional analysis problem.
36.0 m/s 36.0 m OR s ___ s 36.0m
722 mi/hr 722 mi OR hr__ hr 722mi
Writing clean fractions from the denominator
Remember from algebra, that a fraction in the denominator can be multiplied by its reciprocal. Take the following quantities and turn it into a clean fraction as if you were starting a dimensional analysis problem.
52m to 52m s = 0.0715 s 727m/s 1 727m
46mi to 46 mi hr = 0.767 hr 60mi/h 1 60mi
EX 1: Convert 0.083 km/hr to m/s
Given:
Want:
Relationships:
0.083 km/hr
____ m/s
1 km = 1000m
1 hr = 60 min
1 min = 60 sec
1 hr
EX 1: Convert 0.083 km/h to m/s
wantgiven
0.083km 1000m
m/s
1 km
= 2.31 X 10-2
1hr
Relationships1km = 1000m
1h = 60 min
1 min = 60 s
Start with what’s given
60 min 60 s1 min
EX 2: Convert 2.85 g/mL to lb/gal
Given:
Want:
Relationships:
2.85 g/mL
____ lbs/gal
454g = 1lbs
1 gal = 4 quarts
1.06 qts = 1L
1 L = 1000mL
1000mL
EX 2: Convert 2.85 g/mL to lb/gal
wantgiven
2.85 g 1lb
lb/gal
454 g
= 23.7
1mL
Relationships454 g = 1lb
1000mL = 1 L
1.06qt = 1 L
4 qt = 1 gal
Start with what’s given
1 L 1.06 qt
1 L
1 gal
4 qt
1. Convert 3.56 cm/s to ft/hr
Given:
Want:
Relationships:
3.56 cm/s
____ ft/hr
1 ft = 12 in
2.54 cm = 1 in
1 hr = 60 min
1 min = 60 sec
1 ft
1. Convert 3.56 cm/s to ft/h
wantgiven
3.56 cm1 in
ft/hr
2.54 cm
= 420
1 s
Relationships2.54 cm = 1 in
12 in = 1 ft
60 s = 1 min
1 hr = 60 min
Start with what’s given
12 in 1 min
60 s
1 hr
60 min
2. Convert $25.00/feet to cents/cm
Given:
Want:
Relationships:
$25.00/ft
____ cents/cm
$1.00 = 100 cents
1 ft = 12 inches
2.54 cm = 1 in
1 ft
2. Convert $25.00/feet to cents/cm
wantgiven
$ 25.00100 cents
cents/cm
$1
= 82.0
1 ft
Relationships$1 = 100 cents
2.54 cm = 1 in
12 in = 1 ft
Start with what’s given
12 in 2.54 cm
1 in
Solving Word Problems using
Dimensional Analysis
If you are given multiple numbers in a problem, only one number will be your starting point. The
other numbers are relationships that you will use in your problem. If you are given multiple numbers
and one of them involves a “/” (e.g. m/s), then always use the “/” as a relationship and start
with the other number.
If it helps, change any
combination unit into a
relationship
ex. 0.05mL/s0.05mL = 1 s
Given:
Want:
Relationships:
0.05mL/s
____ Liters
1 day = 24 hr
1 hr = 60 min
EX: A faucet is dripping at a rate of 0.05 mL/s. How many liters of water will be
lost in 1 day?
1 day
0.05mL = 1 sec
1000mL = 1 L
60 sec = 1 min
1 min
Relationship
0.05 mL
60 min
EX: A faucet is dripping at a rate of 0.05 mL/s. How many liters of water will be lost in 1 day?
want given
1 day24 hr
L
1 day
= 4.32
1
Relationships0.05 mL = 1 s 60 min = 1
hr
1000mL = 1 L 24 hr = 1 day
60s = 1 minStart with what’s given
1 hr60 s
1 s
1 L1000 mL
Finally, note dimensional analysis can be used anytime
you can say something is equal to something else. It does not have to involve standard conversion factors.
Given:
Want:
Relationships:
____ feet
24 frames = 1 sec
1 hr = 60 min
1 in = 2.54cm
EX 1: Motion pictures are shown at a speed of 24 frames, or individual pictures, each second. If a standard frame is 1.9 cm long, how long will the strand of film be (in ft) for a 2 ½ hr movie?
2.5 hours
1 frame = 1.9cm
1 min = 60 sec
1 ft = 12 in
12 in
EX 1: Motion pictures are shown at a speed of
24 frames, or individual pictures, each second. If a standard
frame is 1.9 cm long, how long will the strand of film be (in
feet) for a 2 ½ hour movie?
1 s
Relationship
1.9 cm60 s
wantrelationship
2.5 hr60 min
ft
1 hr= 13464.6
1
Relationships24 frames = 1 s 1 frame =
1.9cm
1 hr = 60 min 60 s = 1 min
1in = 2.54 cm 1 ft = 12 inStart with what’s given
1 min24 frames
1 frame
1in2.54 cm
want given
1 ft
Given:
Want:
Relationships:
____ trips
60 mi = 1 gal
1 trip = 3.5km
1. The Toyota Prius gets 60 mi/gal of gas. If each trip to school is 3.5 km, how many trips can I make with 10 gallons of gas?
10 gallons
1000m = 1km
1 mile = 1609.3 m
1. The Toyota Prius gets 60 mi/gal of gas. If each
trip to school is 3.5 km, how many trips can I
make with 10 gallons of gas?
1000m
Relationship
1 trip1609.3 m
wantrelationship
10gal 60 mi
trips
1 gal
= 276
1
Relationships60 miles = 1 gal1 trip = 3.5 km
1 mi = 1609.3m 1000m = 1kmStart with what’s given
1 mi1 km
3.5 km
given
Given:
Want:
Relationships:
____ kg
60 s = 1 min
60 min = 1 hr
24 hrs = 1 day
2. Every second 2500 g of sulfuric acid flows out of a
pipe. How many kg of sulfuric acid will flow in 1
day?
1 day
1 sec = 2500g
1kg = 1000g
1 kg1000g
2. Every second 2500 g of sulfuric acid flows
out of a pipe. How many kg of sulfuric acid
will flow in 1 day?
1 min
Relationship
2500g60 min
want
1 day 24 hr
kg
1 day
= 216000
1
Relationships1 s = 2500g 60s = 1 min
1000g = 1kg 60 min = 1 hr
24 hr = 1 day
Start with what’s given
1 hr60 s
1 s
given
Tips for studying• Try doing the review without using
the conversion sheet• Quiz yourself with the conversions• Do extra practice problems (your
textbook may have some)