Dimensional Analysis
Dimensional analysis is a way of problem solving to convert between units using conversion factors
A conversion factor = a ratio of equivalent values used to express the same quantity in different units.
*Set up the bridge
*unit cancellation
*multiply across, Divide down
*round to 2 decimal places (metric – do not round)
Question: Convert 24 in to ft
Steps in dimensional analysis:
Step 1
Step 2
Step 3
1
• Write down the known number and unit
and the unknown unit (the unit you
need to solve for).
• Set up the bridge:
• The unit that goes on the top (the
known unit), is the same one that goes
diagonally on the bottom.
• Write down the conversion factor
• Add converison factors to complete the
bridge.
Step 1
• Known: 24in
• Find: ft
24 in
Step 2
in
•Conversion factor: 1 ft = 12in
1 ft
24 in
Step 3
12 in
24 in
Step 4
• Unit cancellation. Cancel the units that
are diagonal to each other.
• To check your work look to see that you
are left with the units for the unknown.
Step 4
Step 5
• Solve the problem:
• Multiply across, Divide down.
• Round to 2 decimal places
Step 5
1 ft
12 in
2ft
Ch 3 Measurements Notes
METRIC CONVERSIONS USING DIMENSIONAL ANALYSIS:
UNIT Conversion factors:
1 mole = 6.02 X 1023 atoms
2.54cm = 1 inch
1 feet = 12 inches
Will be provided
1 mile = 5280 feet
during Chapter 3
237 mL = 1 cup
test!
1 mL = 1 cm3
3.79 L = 1 gallon
16 cups = 1 gallon
16 ounces = 1 pound
454g = 1 pound
1 gallon = 4 quarts
1 calorie = 4.18 Joules
1 food calories = 1,000 calories
a. 5.7 inches = _____________ cm
Conversion factor:
2.54cm = 1 inch
5.7 inches
2.54 cm
1 inch
=
Set up & solve:
14.48 cm
b. 85 ounces = ________________ pounds
Conversion factor: 16 ounces = 1 pound
85 ounces
1 pound
16 ounces
=
5.31 pounds
c. 125 grams = ______________ pounds
Conversion factor: 454g = 1 pound
125 grams
1 pound
454 grams
Set up & solve:
Set up & solve:
=
0.28 pounds
=
72 mL
d. 72 cm3 = ______________ mL
72 cm3
1 mL
1 cm3
e. 2.5 moles = ______________ atoms
2.50 mole
6.02 X 1023 atoms
1 mole
=
1.505x1024 atoms
f. 24 Joules = ____________ calories
24 Joules
1 calorie
4.18 Joules
=
5.74 calories
g. 6 gallons = _________________ liters
6 gallons
2
3.79 liter
1 gallons
=
22.74 liters
Ch 3 Measurements Notes
METRIC CONVERSIONS USING DIMENSIONAL ANALYSIS:
Write the correct abbreviation for each metric unit. Then underline the prefixes.
1) Kilogram __kg_____
4) Milliliter _mL_______
7)Decameter __dam____
2) Meter _m____
5) Centimeter ___cm____
8) Decijoules_ dJ___
3) Gram ___g___
6) Liter __L_____
9) Milligram ___mg____
mnemonic:
prefix
Kilo (k)
Hecto (h)
Deca (da)
“Unit”
Deci (d)
Centi (c)
Milli (m)
King
Henry
Drinks
Unique
Dark
Chocolate
Milk
mnemonic
Example metric conversion factors:
mL
You need to know how to figure out the
conversion factor for metric conversions.
↔L
hg ↔ cg
1 L = 1000 mL
1 hg = 10,000 cg
km ↔ dm
mm ↔ km
1 km = 10,000 dm
1,000,000mm = 1km
Make the following conversions:
1) 3.4 milliliters to liters
Conversion factor:1000 mL = 1 L
3.4 mL 1L
1000mL
0.0034 L or 3.4x10-3 L
TRY! Make the following metric conversion using dimensional analysis
a. 45 meters to centimeters
Conversion factor:
45 m 100cm
1m
3
1m = 100cm
b. 150cg = ____1.50____ g
Conversion factor: 1g = 100cg
150cg
= 4500 cm
1g
100cg
= 1.50g
Ch 3 Measurements Notes
b. 28km = ______28,000_______ m
Conversion factor: 1km = 1000m
c. 5.0m = ________50_____ dm
Conversion factor: 1 m = 10dm
d. 125kilograms to milligrams
Conversion factor:
1kg = 1000,000mg
125,000,000mg
e.
25 kJ = 250,000 d J
f. 540cm = _____0.0054____km
4
Conversion factor: 1kJ = 10000 dJ
Conversion factor:
1km = 100,000cm
Ch 3 Measurements Notes
Practice B: Real conversions that require more than one conversion factor (two steps). Use real conversion
factors.
Ex: Convert
2 miles to inches. (two-step process)
Conversion factors:
0.25miles = 440yards
1 yard = 36 inches
a. 45 grams = ___________________ounces
Conversion factors:
45 g
1 pounds
454 g
16 ounces
1 pound
=
1.59 oz
b. 2.75 feet = _________________ cm
Conversion factors:
2.75 ft
12 in
1 ft
2.54 cm
1 in
=
83.82 cm
c. 38 quarts = __________________ liters
Conversion factors:
38 quarts
1 gal
4 quarts
3.79 L
1 gal
=
36.01 L
=
56,850 mL
d. 15 gallons = ________________ ml
Conversion factors:
15.00 gal
5
3.79 L
1 gal
1000 mL
1L
Ch 3 Measurements Notes
TRY: Mixed conversions
1. How many meters is 420. inches?
420 in
2.54 cm
=
1,066.80 cm
=
10.67 m
1 in
2.
Convert 5.0kg of flour to pounds.
5.0 kg
l000 g
1 pound
1 kg
=
11.01 lbs
454 g
3. *** Find the distance, in miles, of a 3 km race.
3.0 km
100,000 cm
1 km
1 in
1 ft
1 mile
2.54 cm
12 in
5280 ft
=
1.86 miles
4. ***There are 16 tablespoons (T) in a cup, and 16 cups in a gallon. Find the volume, in L of 8 gallons of
gasoline.
8 gal
6
16 cups
1 gal
16T
1 cup
15mL
1T
=
30,720 mL
=
30.72 L
Ch 3 Measurements Notes