Dimensional
Analysis
How many miles are there in 5 km?
5 km
x
1
1 mi
1.61 km
1mile =
=
5 mi
1.61
=
3.10 mi
1.61 km
Dimensional Analysis Directions:
1. Read the question and identify the problem with
units.
2. Identify the corresponding Conversion Units.
3. Set the conversion units in fraction form so that the
units will cancel with the units you want to get rid of.
4. Cancel units.
5. Multiply across.
6. Check answer and units.
7. Round to appropriate number of significant figures.
Conversion Units
1 inch = 2.54 cm
1 foot = 305 m
1mile=1.61 km
1gram=0.035 oz
1liter=1.06quarts
1 gallon = 3.79 liters
1km=1000m
1 m = 1000 cm
1 hour = 60 min
1 yard = 3 feet
1 lb = 16 oz
John runs one mile in 7.3 minutes. How
many miles per hour does he run?
1 mi x
7.3 min
60 min
1 hr
=
60 mi =
7.3 hr
8.2 mi
hr
1 hour = 60 min
Dimensional Analysis Directions:
1. Read the question and identify the problem with
units.
2. Identify the corresponding Conversion Units.
3. Set the conversion units in fraction form so that the
units will cancel with the units you want to get rid of.
4. Cancel units.
5. Multiply across.
6. Check answer and units.
7. Round to the appropriate number of significant
figures.
Conversion Units
1 inch = 2.54 cm
1 foot = 305 m
1mile=1.61 km
1gram=0.035 oz
1liter=1.06quarts
1 gallon = 3.79 liters
1km=1000m
1 m = 1000 cm
1 hour = 60 min
1 yard = 3 feet
1 lb = 16 oz
If a person drinks 2 liters of soda, how
many gallons is that?
2L
1
x
1 gallon
3.79 L
1 gallon
=
2 gallon = 0.53 gallon
3.79
= 3.79 L
Dimensional Analysis Directions:
1. Read the question and identify the problem with
units.
2. Identify the corresponding Conversion Units.
3. Set the conversion units in fraction form so that the
units will cancel with the units you want to get rid of.
4. Cancel units.
5. Multiply across.
6. Check answer and units.
7. Round to the appropriate number of significant
figures.
Conversion Units
1 inch = 2.54 cm
1 foot = 305 m
1mile=1.61 km
1gram=0.035 oz
1liter=1.06quarts
1 gallon = 3.79 liters
1km=1000m
1 m = 1000 cm
1 hour = 60 min
1 yard = 3 feet
1 lb = 16 oz
If a person eats a 1.0 oz chocolate bar,
how many grams of chocolate is that?
1 oz x
1
1g
0.035 oz
=
1g
0.035
= 28.6 g
1 gram = 0.035 oz
Dimensional Analysis Directions:
1. Read the question and identify the problem with
units.
2. Identify the corresponding Conversion Units.
3. Set the conversion units in fraction form so that the
units will cancel with the units you want to get rid of.
4. Cancel units.
5. Multiply across.
6. Check answer and units.
7. Round to the appropriate number of significant
figures.
Conversion Units
1 inch = 2.54 cm
1 foot = 305 m
1mile=1.61 km
1gram=0.035 oz
1liter=1.06quarts
1 gallon = 3.79 liters
1km=1000m
1 m = 1000 cm
1 hour = 60 min
1 yard = 3 feet
1 lb = 16 oz
If 3 grams of oxygen gas are in a 50 gallon tank,
how many ounces per gallon are in the tank?
3 g x
50 gal
0.035 oz
1g
=
0.105oz =
50 gal
0.0021 oz
gal
1 gram = 0.035 oz
Dimensional Analysis Directions:
1. Read the question and identify the problem with
units.
2. Identify the corresponding Conversion Units.
3. Set the conversion units in fraction form so that the
units will cancel with the units you want to get rid of.
4. Cancel units.
5. Multiply across.
6. Check answer and units.
7. Round to the appropriate number of significant
figures.
Conversion Units
1 inch = 2.54 cm
1 foot = 305 m
1mile=1.61 km
1gram=0.035 oz
1liter=1.06quarts
1 gallon = 3.79 liters
1km=1000m
1 m = 1000 cm
1 hour = 60 min
1 yard = 3 feet
1 lb = 16 oz
How many inches are in 400 cm?
1 in
400 cm x
=
1
2.54 cm
1 in
400 in
2.54
= 157 in
= 2.54 cm
Dimensional Analysis Directions:
1. Read the question and identify the problem with
units.
2. Identify the corresponding Conversion Units.
3. Set the conversion units in fraction form so that the
units will cancel with the units you want to get rid of.
4. Cancel units.
5. Multiply across.
6. Check answer and units.
7. Round to the appropriate number of significant
figures.
Conversion Units
1 inch = 2.54 cm
1 foot = 305 m
1mile=1.61 km
1gram=0.035 oz
1liter=1.06quarts
1 gallon = 3.79 liters
1km=1000m
1 m = 1000 cm
1 hour = 60 min
1 yard = 3 feet
1 lb = 16 oz
How many feet are in 36 km?
36 km
x
1
1 mi
1.61 km
1 mile = 1.61 km
x 5280 ft
= 36 x 5280 = 28.6 ft
1 mi
1.61
1 mile = 5280 ft
Dimensional Analysis Directions:
1. Read the question and identify the problem with
units.
2. Identify the corresponding Conversion Units.
3. Set the conversion units in fraction form so that
the units will cancel with the units you want to
get rid of.
4. Cancel units.
5. Multiply across.
6. Check answer and units.
7. Round to the appropriate number of significant
figures.
Conversion Units
1 inch = 2.54 cm
1 foot = 305 m
1mile=1.61 km
1gram=0.035 oz
1liter=1.06quarts
1 gallon = 3.79 liters
1km=1000m
1 mii = 5280 feet
1 hour = 60 min
1 yard = 3 feet
1 lb = 16 oz