Dimensional Analysis

What is Dimensional Analysis? Dimensional analysis is a problem-solving method that uses the idea that any number or expression can be multiplied by one without changing its value. It is used to go from one unit to another. A conversion factor, or a fraction that is equal to one, is used, along with what you’re given, to determine what the new unit will be.

Conversion Factors Examples Equality- 60 seconds = 1 minute Conversion factors: 60s or 1 min 1 min 60 s Equality- 60 min = 1 hr Conversion factors: 60min or 1 hr 1 hr 60min Any others?

Calculate the number of minutes in 3.61 hours. Dimensional Analysis Calculate the number of minutes in 3.61 hours. *Note: Use the number given in the question to determine the number of sig figs in your answer. 1. Write the given. 2. Draw the chart.

3. Think of a relationship: 1 hr = 60 min 4. Cancel units diagonally. Dimensional Analysis Calculate the number of minutes in 3.61 hours. *Note: Use the number given in the question to determine the number of sig figs in your answer. 3. Think of a relationship: 1 hr = 60 min 4. Cancel units diagonally.

5. Add the rest of the relationship. Dimensional Analysis Calculate the number of minutes in 3.61 hours. 5. Add the rest of the relationship. Multiply across and divide by the bottom Count sig figs in the given. Round the answer to that number of sig figs.

Conversion Factor: 1 in= 2.54 cm Dimensional Analysis How many centimeters are in 4.2 inches? *Note: Use the number given in the question to determine the number of sig figs in your answer. Conversion Factor: 1 in= 2.54 cm

How many centimeters are in 4.2 inches? Dimensional Analysis How many centimeters are in 4.2 inches? *Note: Use the number given in the question to determine the number of sig figs in your answer.

Realize that we don’t know just one step from weeks to seconds. Dimensional Analysis Multi-Step Problems Calculate the number of seconds in two weeks. Realize that we don’t know just one step from weeks to seconds.

Dimensional Analysis Multi-Step Problems Start as usual. Calculate the number of seconds in two weeks. Start as usual.

Dimensional Analysis Multi-Step Problems Extend your table. Calculate the number of seconds in two weeks. Extend your table.

Continue adding relationships. Dimensional Analysis Multi-Step Problems Calculate the number of seconds in two weeks. Continue adding relationships.

Add as many conversions as needed. Dimensional Analysis Multi-Step Problems Calculate the number of seconds in two weeks. Round to 1 sig fig. Add as many conversions as needed.

Notice the use of the bottom space. Dimensional Analysis Multi-Step Problems Convert the density of 0.58 g/mL to lb/gallon. (1 L = 1.057 qt and 4 qt = 1 gal; 1kg = 2.2 lb) Notice the use of the bottom space.

Ignore the bottom unit for a moment. Dimensional Analysis Multi-Step Problems Convert the density of 0.58 g/mL to lb/gallon. (1 L = 1.057 qt and 4 qt = 1 gal; 1kg = 2.2 lb) Ignore the bottom unit for a moment. Concentrate on converting the top unit.

Continue converting the top. Stop when you get to lb…the goal. Dimensional Analysis Multi-Step Problems Convert the density of 0.58 g/mL to lb/gallon. (1 L = 1.057 qt and 4 qt = 1 gal; 1kg = 2.2 lb) Continue converting the top. Stop when you get to lb…the goal.

Now, focus on the bottom units. Dimensional Analysis Multi-Step Problems Convert the density of 0.58 g/mL to lb/gallon. (1 L = 1.057 qt and 4 qt = 1 gal; 1kg = 2.2 lb) Now, focus on the bottom units. It is OK to cancel units from a distance.

Continue adding until you reach the goal. Dimensional Analysis Multi-Step Problems Convert the density of 0.58 g/mL to lb/gallon. (1 L = 1.057 qt and 4 qt = 1 gal; 1kg = 2.2 lb) Continue adding until you reach the goal.

If a pound of apples costs $0.79, then 5.3 lbs will cost _________. Fill-In iRespond Question If a pound of apples costs $0.79, then 5.3 lbs will cost _________. Give your answer to TWO decimal places which is customary with money. A.) 4.19;; B.) C.) D.) E.)

1849 yards = __________ miles Hint: 5280 ft = 1 mile Fill-In iRespond Question 1849 yards = __________ miles Hint: 5280 ft = 1 mile Give your answer to 4 sig figs. A.) 1.051;; B.) C.) D.) E.)

Give your answer to TWO sig figs. Fill-In iRespond Question If Boston and New York City are 190 miles apart, then the distance between the two cities is _______ km. Hint: 1 km = 0.621 miles Give your answer to TWO sig figs. A.) 310;; B.) C.) D.) E.)

Give your answer to THREE sig figs. Fill-In iRespond Question If a pound of apples costs $0.79, then a shopper with $2.00 will be able to purchase ________ lbs of apples. Give your answer to THREE sig figs. A.) 2.53;; B.) C.) D.) E.)

F Fill-In iRespond Question If a US car advertisement brags that an SVU gets 26 miles/gallon on the highway, then the same car would be described in Europe as getting ___________ km/L. Hint: 1 L = 1.057 qt; 4 qt = 1 gal; 1 km = 0.621 miles Give your answer to TWO sig figs. A.) 11;; B.) C.) D.) E.)