US Conversion Steps (Dimensional Analysis)

1. US Conversion Steps(Dimensional Analysis) • Read the question to figure out what you have/know for information. The question will provide you with information that identifies your starting point and your final destination. • Starting point = the number and unit provided by the question • Final destination = the units desired after converting • Using the information gathered from the question, write your starting point and your final destination. • Determine the means in which you will get from your starting point to your final destination (simply find “connections” or conversion factors between your starting and final unit). • Create a fraction by placing your starting point over one. • Multiply between fractions. • Write in the bottom unit of the new fraction. This should be the same as the top unit of the previous fraction. • Write one set of “connections” or conversion factors into the fraction. Your bottom unit will guide you. • Ask yourself, “Do I have the desired unit (final destination) on the top of the new fraction?” NO YES • Cancel any units that are diagonal. (This should leave you with only the units that represent your final destination) • Multiply the top of the fractions…multiply the bottom of the fractions…divide the top by the bottom. (Go back to step 5) (Proceed to step 9)

2. Practice Conversions • How many seconds are in 6 minutes? 2. How many centimeters are in 27 inches? • If a truck weighs 15,356 pounds, how many tons is it? 4. If you had 10.5 gallons of milk, how many pints would you have? 5. Students go to school for 180 days. How many minutes is this equal to?

3. How many seconds are in 6 minutes? Final Destination Starting Point 6 minutes  seconds Step 1 – Read the question and determine what information it provides you with (starting point & final destination) Step 2 – Write down your starting point and your final destination 1 minute = 60 seconds Step 3 – Determine how you will get from your starting point to your final destination (list any “connections” or conversion factors) ( ) ( ) (6 minutes) 1 60 seconds (6)(60 seconds) = 1 minute (1)(1) Step 9 – Cancel all diagonal units. Once this is done, your final destination should be the only unit left – in this case seconds Step 5 – Multiply between fractions = Step 10 – Multiply the top of the fractions; multiply the bottom of the fractions; divide the product of the top by the product of the bottom 360 seconds Step 8 – Determine if this top unit is the desired unit (your final destination). In this case the answer is YES, so we move on to step 9 Step 7 – Write the appropriate conversion factor into the fraction. Your bottom unit will guide you. Step 6 – Write in the bottom unit of the new fraction (this is the same as the top unit of your previous fraction) Step 4 – Create a fraction by placing your starting point over one

4. How many centimeters are in 27 inches? Final Destination Starting Point 27 inches  centimeters Step 1 – Read the question and determine what information it provides you with (starting point & final destination) Step 2 – Write down your starting point and your final destination 1 inch = 2.54 centimeters Step 3 – Determine how you will get from your starting point to your final destination (list any “connections” or conversion factors) ( ) ( ) 2.54 cm (27)(2.54 cm) (27 inches) 1 = (1)(1) 1 inch Step 9 – Cancel all diagonal units. Once this is done, your final destination should be the only unit left – in this case centimeters Step 5 – Multiply between fractions = Step 10 – Multiply the top of the fractions; multiply the bottom of the fractions; divide the product of the top by the product of the bottom 68.58 centimeters Step 8 – Determine if this top unit is the desired unit (your final destination). In this case the answer is YES, so we move on to step 9 Step 7 – Write the appropriate conversion factor into the fraction. Your bottom unit will guide you. Step 6 – Write in the bottom unit of the new fraction (this is the same as the top unit of your previous fraction) Step 4 – Create a fraction by placing your starting point over one

5. If a truck weighs 15,356 pounds, how many tons is it? Final Destination Starting Point 15,356 pounds  tons Step 1 – Read the question and determine what information it provides you with (starting point & final destination) Step 2 – Write down your starting point and your final destination 2000 pounds = 1 ton Step 3 – Determine how you will get from your starting point to your final destination (list any “connections” or conversion factors) ( ) ( ) (15,356 lbs.) 1 1 ton (15,356)(1 ton) = (1)(2000) 2000 lbs. Step 9 – Cancel all diagonal units. Once this is done, your final destination should be the only unit left – in this case tons Step 5 – Multiply between fractions = 7.678 tons Step 10 – Multiply the top of the fractions; multiply the bottom of the fractions; divide the product of the top by the product of the bottom Step 8 – Determine if this top unit is the desired unit (your final destination). In this case the answer is YES, so we move on to step 9 Step 7 – Write the appropriate conversion factor into the fraction. Your bottom unit will guide you. Step 6 – Write in the bottom unit of the new fraction (this is the same as the top unit of your previous fraction) Step 4 – Create a fraction by placing your starting point over one

6. If you had 10.5 gallons of milk, how many pints would you have? Final Destination Starting Point 10.5 gallons  pints Step 1 – Read the question and determine what information it provides you with (starting point & final destination) Step 2 – Write down your starting point and your final destination 1 gallon = 4 quarts 1 quart = 2 pints Step 3 – Determine how you will get from your starting point to your final destination (list any “connections” or conversion factors) ( ) ( ) ( ) ( ) (10.5 gallons) 1 4 quarts 2 pints 1 gallon 1 quart (10.5)(4)(2 pints) Step 5 – Multiply between fractions Step 7 – Write the appropriate conversion factor into the fraction. Your bottom unit will guide you. Step 10 – Multiply the top of the fractions; multiply the bottom of the fractions; divide the product of the top by the product of the bottom = Step 6 – Write in the bottom unit of the new fraction (this is the same as the top unit of your previous fraction) Step 5 – Multiply between fractions Step 7 – Write the appropriate conversion factor into the fraction. Your bottom unit will guide you. Step 8 – Determine if this top unit is the desired unit (your final destination). In this case the answer is YES, so we move on to step 9 84 pints Step 8 – Determine if this top unit is the desired unit (your final destination). In this case the answer is NO, so we move back to step 5 Step 9 – Cancel all diagonal units. Once this is done, your final destination should be the only unit left – in this case pints = (1)(1)(1) Step 6 – Write in the bottom unit of the new fraction (this is the same as the top unit of your previous fraction) Step 4 – Create a fraction by placing your starting point over one

7. Students go to school for 180 days. How many minutes is this equal to? Final Destination Starting Point 180 days  minutes Step 1 – Read the question and determine what information it provides you with (starting point & final destination) Step 2 – Write down your starting point and your final destination 1 day = 24 hours 1 hour = 60 minutes Step 3 – Determine how you will get from your starting point to your final destination (list any “connections” or conversion factors) ( ) ( ) 24 hours ( ) ( ) 60 (180 days) 1 minutes day 1 hour 1 Step 9 – Cancel all diagonal units. Once this is done, your final destination should be the only unit left – in this case minutes (180)(24)(60 minutes) Step 5 – Multiply between fractions Step 5 – Multiply between fractions Step 10 – Multiply the top of the fractions; multiply the bottom of the fractions; divide the product of the top by the product of the bottom = Step 6 – Write in the bottom unit of the new fraction (this is the same as the top unit of your previous fraction) Step 7 – Write the appropriate conversion factor into the fraction. Your bottom unit will guide you. Step 7 – Write the appropriate conversion factor into the fraction. Your bottom unit will guide you. 259,200 minutes = Step 8 – Determine if this top unit is the desired unit (your final destination). In this case the answer is NO, so we move back to step 5 Step 6 – Write in the bottom unit of the new fraction (this is the same as the top unit of your previous fraction) (1)(1)(1) Step 4 – Create a fraction by placing your starting point over one Step 8 – Determine if this top unit is the desired unit (your final destination). In this case the answer is YES, so we move on to step 9

8. Answers • How many seconds are in 6 minutes? 360 seconds • How many centimeters are in 27 inches? 68.58 centimeters • If a truck weighs 15,356 pounds, how many tons is it? 7.678 tons • If you had 10.5 gallons of milk, how many pints would you have? 84 pints • Students go to school for 180 days. How many minutes is this equal to? 259,200 minutes

9. Online Tutorials • http://www2.wwnorton.com/college/chemistry/gilbert/tutorials/ch1.htm (click on “view tutorial” for dimensional analysis) • http://www.wfu.edu/~ylwong/chem/dimensionanalysis/practice/index.html (click on examples under dimensional analysis on the left side of the page) • http://chemistry.alanearhart.org/Tutorials/DimAnal/ Interactive Quiz • http://chem.lapeer.org/Exams/DimAnalQuiz.html