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Dimensional Analysis
Factor Labeling
Dimensional Analysis
• This is a method of problem-solving which ___focuses______ on the units.
Dimensional Analysis
• This is a method of problem-solving which ___focuses______ on the units.
• Helps you set up equations correctly → Solve for units as wells as numbers
Dimensional Analysis
• ____A conversion factor___________ is a ratio of equivalent values used to express the same quantity in different units.
Dimensional Analysis
• ____A conversion factor___________ is a ratio of equivalent values used to express the same quantity in different units.
• Always equal to __1____.
Dimensional Analysis
• ____A conversion factor___________ is a ratio of equivalent values used to express the same quantity in different units.
• Always equal to __1____.
• Used to convert from one unit to the other.
Dimensional Analysis
Set up the problem so the units will cancel as you solve it.
Dimensional Analysis
Example: 1 Liter = 1000 milliliters
Dimensional Analysis
Example: 1 Liter = 1000 milliliters
This equality can be converted into __2__ conversion factors
Dimensional Analysis
Example: 1 Liter = 1000 milliliters
This equality can be converted into __2__ conversion factors.
1 L or 1000 mL
Dimensional Analysis
Example: 1 Liter = 1000 milliliters
This equality can be converted into __2__ conversion factors.
1 L or 1000 mL 1000 mL 1 L
To solve problems with dimensional analysis:
1. Put given value on __top__ of fraction bar
To solve problems with dimensional analysis:
1. Put given value on __top__ of fraction bar
2. Determine what __conversion factor__ you can use that has both the given unit & ______desired__ unit.
To solve problems with dimensional analysis:
1. Put given value on __top__ of fraction bar
2. Determine what __conversion factor__ you can use that has both the given unit & ______desired__ unit.
3. Set up conversion factor with __desired unit_ on top and ___given__ unit on __bottom__ so given units cancel.
Example: Convert 65.22 mg to ___g
1. Given: __65.22 mg __
Example: Convert 65.22 mg to ___g
1. Given: __65.22 mg __
2. Equality: __1 g = 1000 mg__
Example: Convert 65.22 mg to ___g
1. Given: __65.22 mg __
2. Equality: __1 g = 1000 mg__ so…. 2 conversion factors: 1 g or 1000 mg
Example: Convert 65.22 mg to ___g
1. Given: __65.22 mg __
2. Equality: __1 g = 1000 mg__ so…. 2 conversion factors: 1 g or 1000 mg 1000 mg 1 g
Example: Convert 65.22 mg to ___g
1. Given: __65.22 mg __
2. Equality: __1 g = 1000 mg__ so…. 2 conversion factors: 1 g or 1000 mg 1000 mg 1 g
3. 65.22 mg
Example: Convert 65.22 mg to ___g
1. Given: __65.22 mg __
2. Equality: __1 g = 1000 mg__ so…. 2 conversion factors: 1 g or 1000 mg 1000 mg 1 g
3. 65.22 mg {pick a conversion factor so that the given units (mg) cancel}
Example: Convert 65.22 mg to ___g
1. Given: __65.22 mg __
2. Equality: __1 g = 1000 mg__ so…. 2 conversion factors: 1 g or 1000 mg 1000 mg 1 g
3. 65.22 mg
Example: Convert 65.22 mg to ___g
1. Given: __65.22 mg __
2. Equality: __1 g = 1000 mg__ so…. 2 conversion factors: 1 g or 1000 mg 1000 mg 1 g
3. 65.22 mg 1 g 1000 mg
Example: Convert 65.22 mg to ___g
1. Given: __65.22 mg __
2. Equality: __1 g = 1000 mg__ so…. 2 conversion factors: 1 g or 1000 mg 1000 mg 1 g
3. 65.22 mg 1 g = 0.06522 g 1000 mg
Practice: 0.84 m to _____ cmGiven: __0.84 m__
Practice: 0.84 m to _____ cmGiven: __0.84 m__
Equality: 1 m = 100 cm
which unit should go on the bottom?
Practice: 0.84 m to _____ cmGiven: __0.84 m__
Equality: 1 m = 100 cm
which unit should go on the bottom?
Answer: the unit you want to cancel: m
Practice: 0.84 m to _____ cmGiven: __0.84 m__
Equality: 1 m = 100 cm
which unit should go on the bottom?
Answer: the unit you want to cancel: m
so use: 100 cm1 m
Practice: 0.84 m to _____ cmGiven: __0.84 m__
so use: 100 cm1 m
0.84 m
Practice: 0.84 m to _____ cmGiven: __0.84 m__
so use: 100 cm1 m
0.84 m 100 cm 1 m
Practice: 0.84 m to _____ cmGiven: __0.84 m__
so use: 100 cm1 m
0.84 m 100 cm = 84 cm 1 m
Practice: 5.5 dozen eggs to single eggs
Given: 5.5 doz
Practice: 5.5 dozen eggs to single eggs
Given: 5.5 doz
Equality: 1 doz = 12 eggs
Practice: 5.5 dozen eggs to single eggs
Given: 5.5 doz
Equality: 1 doz = 12 eggs
We want doz to cancel:
Practice: 5.5 dozen eggs to single eggs
Given: 5.5 doz
Equality: 1 doz = 12 eggs
We want doz to cancel:
so put doz on bottom
Practice: 5.5 dozen eggs to single eggs
Given: 5.5 doz
Equality: 1 doz = 12 eggs
We want doz to cancel:
so use: 12 eggs 1 doz
Practice: 5.5 dozen eggs to single eggs
Given: 5.5 doz
5.5 doz
Practice: 5.5 dozen eggs to single eggs
Given: 5.5 doz
5.5 doz 12 eggs1 doz
Practice: 5.5 dozen eggs to single eggs
Given: 5.5 doz
5.5 doz 12 eggs = 66 eggs1 doz
Practice: 5.5 dozen eggs to single eggs
Given: 5.5 doz
5.5 doz 12 eggs = 66 eggs1 doz
conversion factors do not affect the number of sig figs in answer *start with 2 sig figs = end with 2
Sometimes you may need more than __1___conversion factor
Ex: Convert 2.01 miles to ___inches
1 mile = 5280 feet
2.01 miles
Ex: Convert 2.01 miles to ___inches
1 mile = 5280 feet
2.01 miles
Ex: Convert 2.01 miles to ___inches
1 mile = 5280 feet
2.01 miles 1 mile
Ex: Convert 2.01 miles to ___inches
1 mile = 5280 feet
2.01 miles 5280 feet 1mile
Ex: Convert 2.01 miles to ___inches
1 mile = 5280 feet
2.01 miles 5280 feet 1mile
Ex: Convert 2.01 miles to ___inches
1 mile = 5280 feet
2.01 miles 5280 feet 1mile
Now our answer is in feet…but we want inches
So…we need another step!!
Ex: Convert 2.01 miles to ___inches
1 mile = 5280 feet
2.01 miles 5280 feet 1mile
Ex: Convert 2.01 miles to ___inches
1 mile = 5280 feet
2.01 miles 5280 feet 1mile feet
Ex: Convert 2.01 miles to ___inches
1 mile = 5280 feet
2.01 miles 5280 feet 12 inches 1mile 1 feet
Ex: Convert 2.01 miles to ___inches
1 mile = 5280 feet
2.01 miles 5280 feet 12 inches 1mile 1 feet
Ex: Convert 2.01 miles to ___inches
1 mile = 5280 feet
2.01 miles 5280 feet 12 inches = 127353 inches 1 mile 1 feet
Ex: Convert 2.01 miles to ___inches
1 mile = 5280 feet
2.01 miles 5280 feet 12 inches = 127353 inches 1 mile 1 feet
Need correct # of sig figs!!!
Ex: Convert 2.01 miles to ___inches
1 mile = 5280 feet
2.01 miles 5280 feet 12 inches = 127353 inches 1 mile 1 feet
Need correct # of sig figs!!! conversion factors do not affect the number of sig figs in answer
*start with 3 sig figs = end with 3
Ex: Convert 2.01 miles to ___inches
1 mile = 5280 feet 127000
2.01 miles 5280 feet 12 inches = 127353 inches 1 mile 1 feet
Need correct # of sig figs!!! conversion factors do not affect the number of sig figs in answer
*start with 3 sig figs = end with 3
834 hours to ___ months
834 hr
834 hours to ___ months
834 hr hr
Hours has to go on bottom to cancel, but I don’t know an hours to month conversion factor
834 hours to ___ months
834 hr hr
Hours has to go on bottom to cancel, but I don’t know an hours to month conversion factor
But I do know hours to what?
834 hours to ___ months
834 hr 1 day 24 hr
834 hours to ___ months
834 hr 1 day 24 hr
Now my unit is day, but I need month…so I need another step
834 hours to ___ months
834 hr 1 day 24 hr
What unit must go in the bottom of the next step?
834 hours to ___ months
834 hr 1 day 24 hr day
What is my day to month conversion factor?
834 hours to ___ months
834 hr 1 day 1 month 24 hr 30 days
834 hours to ___ months
834 hr 1 day 1 month = 1.158 months 24 hr 30 days
How many sig figs should there be in answer?
834 hours to ___ months
834 hr 1 day 1 month = 1.158 months 24 hr 30 days 1.16 months
How many sig figs should there be in answer? 3
0.143 hours to ____ seconds
0.143 hr
0.143 hours to ____ seconds
0.143 hr1 hr
0.143 hours to ____ seconds
0.143 hr 60 min1 hr
0.143 hours to ____ seconds
0.143 hr 60 min1 hr
0.143 hours to ____ seconds
0.143 hr 60 min1 hr
0.143 hours to ____ seconds
0.143 hr 60 min1 hr min
0.143 hours to ____ seconds
0.143 hr 60 min sec1 hr min
0.143 hours to ____ seconds
0.143 hr 60 min 60 sec1 hr 1 min
0.143 hours to ____ seconds
0.143 hr 60 min 60 sec = 514.8 seconds1 hr 1 min
0.143 hours to ____ seconds
0.143 hr 60 min 60 sec = 514.8 seconds1 hr 1 min 515 sec
3 sig figs!!
