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Dimensional Analysis Factor Labeling

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Dimensional Analysis This is a method of problem-solving which ___focuses______ on the units.

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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

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Dimensional Analysis ____A conversion factor___________ is a ratio of equivalent values used to express the same quantity in different units.

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Dimensional Analysis ____A conversion factor___________ is a ratio of equivalent values used to express the same quantity in different units. Always equal to __1____.

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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.

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Dimensional Analysis Set up the problem so the units will cancel as you solve it.

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Dimensional Analysis Example: 1 Liter = milliliters

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Dimensional Analysis Example: 1 Liter = 1000 milliliters This equality can be converted into __2__ conversion factors

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Dimensional Analysis Example: 1 Liter = 1000 milliliters This equality can be converted into __2__ conversion factors. 1 L or 1000 mL

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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

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**To solve problems with dimensional analysis:**

Put given value on __top__ of fraction bar

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**To solve problems with dimensional analysis:**

Put given value on __top__ of fraction bar Determine what __conversion factor__ you can use that has both the given unit & ______desired__ unit.

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**To solve problems with dimensional analysis:**

Put given value on __top__ of fraction bar Determine what __conversion factor__ you can use that has both the given unit & ______desired__ unit. Set up conversion factor with __desired unit_ on top and ___given__ unit on __bottom__ so given units cancel.

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**Example: Convert 65.22 mg to ___g**

Given: __65.22 mg __

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**Example: Convert 65.22 mg to ___g**

Given: __65.22 mg __ Equality: __1 g = 1000 mg__

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**Example: Convert 65.22 mg to ___g**

Given: __65.22 mg __ Equality: __1 g = 1000 mg__ so…. 2 conversion factors: 1 g or mg

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**Example: Convert 65.22 mg to ___g**

Given: __65.22 mg __ Equality: __1 g = 1000 mg__ so…. 2 conversion factors: 1 g or mg mg g

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**Example: Convert 65.22 mg to ___g**

Given: __65.22 mg __ Equality: __1 g = 1000 mg__ so…. 2 conversion factors: 1 g or mg mg g 65.22 mg

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**Example: Convert 65.22 mg to ___g**

Given: __65.22 mg __ Equality: __1 g = 1000 mg__ so…. 2 conversion factors: 1 g or mg mg g 65.22 mg {pick a conversion factor so that the given units (mg) cancel}

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**Example: Convert 65.22 mg to ___g**

Given: __65.22 mg __ Equality: __1 g = 1000 mg__ so…. 2 conversion factors: 1 g or mg mg g 65.22 mg

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**Example: Convert 65.22 mg to ___g**

Given: __65.22 mg __ Equality: __1 g = 1000 mg__ so…. 2 conversion factors: 1 g or mg mg g 65.22 mg g 1000 mg

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**Example: Convert 65.22 mg to ___g**

Given: __65.22 mg __ Equality: __1 g = 1000 mg__ so…. 2 conversion factors: 1 g or mg mg g 65.22 mg g = g 1000 mg

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Practice: m to _____ cm Given: __0.84 m__

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Practice: m to _____ cm Given: __0.84 m__ Equality: 1 m = 100 cm which unit should go on the bottom?

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Practice: m to _____ cm Given: __0.84 m__ Equality: 1 m = 100 cm which unit should go on the bottom? Answer: the unit you want to cancel: m

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Practice: m to _____ cm Given: __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 cm 1 m

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Practice: m to _____ cm Given: __0.84 m__ so use: 100 cm 1 m 0.84 m

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Practice: m to _____ cm Given: __0.84 m__ so use: 100 cm 1 m 0.84 m 100 cm

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Practice: m to _____ cm Given: __0.84 m__ so use: 100 cm 1 m 0.84 m 100 cm = 84 cm

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**Practice: 5.5 dozen eggs to single eggs**

Given: 5.5 doz

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**Practice: 5.5 dozen eggs to single eggs**

Given: 5.5 doz Equality: 1 doz = 12 eggs

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**Practice: 5.5 dozen eggs to single eggs**

Given: 5.5 doz Equality: 1 doz = 12 eggs We want doz to cancel:

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**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

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**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

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**Practice: 5.5 dozen eggs to single eggs**

Given: 5.5 doz 5.5 doz

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**Practice: 5.5 dozen eggs to single eggs**

Given: 5.5 doz 5.5 doz 12 eggs 1 doz

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**Practice: 5.5 dozen eggs to single eggs**

Given: 5.5 doz 5.5 doz eggs = 66 eggs 1 doz

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**Practice: 5.5 dozen eggs to single eggs**

Given: 5.5 doz 5.5 doz eggs = 66 eggs 1 doz conversion factors do not affect the number of sig figs in answer *start with 2 sig figs = end with 2

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**Sometimes you may need more than __1___conversion factor**

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**Ex: Convert 2.01 miles to ___inches**

1 mile = 5280 feet 2.01 miles

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**Ex: Convert 2.01 miles to ___inches**

1 mile = 5280 feet 2.01 miles

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**Ex: Convert 2.01 miles to ___inches**

1 mile = 5280 feet 2.01 miles 1 mile

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**Ex: Convert 2.01 miles to ___inches**

1 mile = 5280 feet 2.01 miles 5280 feet 1mile

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**Ex: Convert 2.01 miles to ___inches**

1 mile = 5280 feet 2.01 miles 5280 feet 1mile

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**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!!

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**Ex: Convert 2.01 miles to ___inches**

1 mile = 5280 feet 2.01 miles 5280 feet 1mile

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**Ex: Convert 2.01 miles to ___inches**

1 mile = 5280 feet 2.01 miles 5280 feet 1mile feet

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**Ex: Convert 2.01 miles to ___inches**

1 mile = 5280 feet 2.01 miles 5280 feet 12 inches 1mile 1 feet

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**Ex: Convert 2.01 miles to ___inches**

1 mile = 5280 feet 2.01 miles 5280 feet 12 inches 1mile 1 feet

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**Ex: Convert 2.01 miles to ___inches**

1 mile = 5280 feet 2.01 miles 5280 feet 12 inches = inches 1 mile 1 feet

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**Ex: Convert 2.01 miles to ___inches**

1 mile = 5280 feet 2.01 miles 5280 feet 12 inches = inches 1 mile 1 feet Need correct # of sig figs!!!

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**Ex: Convert 2.01 miles to ___inches**

1 mile = 5280 feet 2.01 miles 5280 feet 12 inches = 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

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**Ex: Convert 2.01 miles to ___inches**

1 mile = 5280 feet miles 5280 feet 12 inches = 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

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834 hours to ___ months 834 hr

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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

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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?

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834 hours to ___ months 834 hr 1 day 24 hr

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834 hours to ___ months 834 hr 1 day 24 hr Now my unit is day, but I need month…so I need another step

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834 hours to ___ months 834 hr 1 day 24 hr What unit must go in the bottom of the next step?

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834 hours to ___ months 834 hr 1 day 24 hr day What is my day to month conversion factor?

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834 hours to ___ months 834 hr 1 day 1 month 24 hr 30 days

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834 hours to ___ months 834 hr 1 day 1 month = months 24 hr 30 days How many sig figs should there be in answer?

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834 hours to ___ months 834 hr 1 day 1 month = months 24 hr 30 days 1.16 months How many sig figs should there be in answer? 3

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0.143 hours to ____ seconds 0.143 hr

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0.143 hours to ____ seconds 0.143 hr 1 hr

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0.143 hours to ____ seconds 0.143 hr 60 min 1 hr

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0.143 hours to ____ seconds 0.143 hr 60 min 1 hr

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0.143 hours to ____ seconds 0.143 hr 60 min 1 hr

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0.143 hours to ____ seconds 0.143 hr 60 min 1 hr min

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0.143 hours to ____ seconds 0.143 hr 60 min sec 1 hr min

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0.143 hours to ____ seconds 0.143 hr 60 min 60 sec 1 hr 1 min

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0.143 hours to ____ seconds 0.143 hr 60 min 60 sec = seconds 1 hr 1 min

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0.143 hours to ____ seconds 0.143 hr 60 min 60 sec = seconds 1 hr 1 min 515 sec 3 sig figs!!

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Using the Factor Label Method. “That costs five.”

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