Dimensional Analysis

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: • Put given value on __top__ of fraction bar

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.

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.

Example: Convert 65.22 mg to ___g • Given: __65.22 mg __

Example: Convert 65.22 mg to ___g • Given: __65.22 mg __ • Equality: __1 g = 1000 mg__

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

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

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

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

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

Example: Convert 65.22 mg to ___g • Given: __65.22 mg __ • Equality: __1 g = 1000 mg__ so…. 2 conversion factors: 1 g or 1000 mg 1000 mg 1 g • 65.22 mg 1 g = 0.06522 g 1000 mg

Practice: 0.84 m to _____ cm Given: __0.84 m__

Practice: 0.84 m to _____ cm Given: __0.84 m__ Equality: 1 m = 100 cm which unit should go on the bottom?

Practice: 0.84 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

Practice: 0.84 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

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

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

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

Practice: 5.5 dozen eggs to single eggs Given: 5.5 doz 5.5 doz 12 eggs = 66 eggs 1 doz

Practice: 5.5 dozen eggs to single eggs Given: 5.5 doz 5.5 doz 12 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

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 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 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

Dimensional Analysis