What is Dimensional Analysis? Dimensional Analysis (also called Factor-Label Method or the Unit Factor Method) is a problem-solving method that uses the fact that any number or expression can be multiplied by one without changing its value!

Dimensional Analysis is not for everyone. But it's probably for you Dimensional Analysis is not for everyone. But it's probably for you. First of all then, who should avoid Dimensional Analysis (DA)?

Reasons for not using Dimensional Analysis 1. Let's say you're super-intelligent and enjoy solving relatively simple problems in the most complex manner.

Reasons for not using Dimensional Analysis 2. Let's say you're tired of always getting the correct answers.

Reasons for not using Dimensional Analysis 3. Let's say you're an arty type and you can't be confined by the structure of DA. You like messy solutions scribbled all over the page in every which direction. It's not that you want to make a mistake, but you really don't care that much about the answer. You just like the abstract design created by the free-wheeling solution... and the freedom from being confined by structure.

Reasons for not using Dimensional Analysis 4. Let's say that you have no interest in going to the prom or making the soccer team, and you don't mind being unpopular, unattractive, ignorant, insecure, uninformed, and unpleasant.

Otherwise, You Need Dimensional Analysis!

Equalities State the same measurement in two different units 10.0 in. 25.4 cm

Some Metric Equalities Examples Length 1 m = 100 cm Mass 1 kg = 1000 g Volume 1 L = 1000 mL

Some American Equalities Examples 1 ft = 12 inches 1 lb = 16 oz 1 quart = 2 pints 1 quart = 4 cups The quantities in each pair give the same measured amount in two different units.

Some Metric-American Equalities Examples 1 in. = 2.54 cm 1 qt = 946 mL 1 L = 1.06 qt 1 lb = 454 g 1 kg = 2.20 lb

An equality expressed as a fraction Conversion Factors An equality expressed as a fraction ALWAYS EQUAL TO ONE!!!!!!!!!! Example: 1 in. = 2.54 cm Factors: 1 in. and 2.54 cm 2.54 cm 1 in.

Learning Check A. Liters and mL B. Hours and minutes Write conversion factors that relate each of the following pairs of units: A. Liters and mL B. Hours and minutes

Solution A. Liters and mL 1 L = 1000 mL 1 L and 1000 mL 1000 mL 1 L B. hours and minutes 1 hr = 60 min 1 hr and 60 min 60 min 1 hr

Steps for solving problems- Write a “?” followed by the unit you are being asked for. 2. Write an”=” sign. 3. Write the number and unit you are given to start with.

Steps for solving problems- 4. Use conversion factors that will cancel out unwanted units until only the unit you want is left. 5. Multiply all numbers on top. Multiply all numbers on bottom. Divide last. 6. Write final answer with units.

Practice- How many centimeters are in 6.00 inches? (2) Express 24.0 cm in inches.

You can also string many unit factors together: Practice- Susanna is 5.50 ft tall. What is her height in millimeters? Conversions to use: 1 in = 2.54 cm 12 in = 1 ft 10 mm = 1 cm Unit Plan: Solve:

(2) How many seconds are in 2.0 years? Conversions to use: 1 yr = 365 days 1 day = 24 hr 1 hr = 60 min 1 min = 60 s Unit Plan: Solve: