dimensional analysis factor labeling. dimensional analysis this is a method of problem-solving which...

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!!