Unit Conversions

1. Unit Conversions • Units are Wonderful and Horrible! • Do unit conversions when you want an answer in different units than the original information you have • Familiar Units • Salary: dollars per hour [$/hr --> $/year] • Price: dollars per pound [$/lb --> $/turkey] • Speed: miles per hour [m/h, or miles/trip] • Examples of “Unity” fractions (ones that equal “1”) • Time: minutes per hour [60 min/1 hour] • Weight: ounces per pound [16 oz/1 lb]

2. Example: Salary • It all boils down to multiplying your starting info by a series of “unity” fractions (1) , set up to get the final units you want • When you add “units” (words) to fractions, you can treat them just like numbers, i.e. cancel matching units (1) (1) (1) (1) 20$ x 8 hours x 5 days x 4 weeks x 12 months hour day week month year

3. Cancel Units • It all boils down to multiplying your starting info by a series of “unity” fractions (1) , set up to get the final units you want • When you add units (“words”) to fractions, you can treat them just like numbers (1) (1) (1) (1) 20$ x 8 hours x 5 days x 4 weeks x 12 months hour day week month year

4. Cancel … • It all boils down to multiplying your starting info by a series of “unity” fractions (1) , set up to get the final units you want • When you add units (“words”) to fractions, you can treat them just like numbers (1) (1) (1) (1) 20$ x 8 hours x 5 days x 4 weeks x 12 months hour day week month year

5. Cancel … • It all boils down to multiplying your starting info by a series of “unity” fractions (1) , set up to get the final units you want • When you add units (“words”) to fractions, you can treat them just like numbers (1) (1) (1) (1) 20$ x 8 hours x 5 days x 4 weeks x 12 months hour day week month year

6. Cancel … • It all boils down to multiplying your starting info by a series of “unity” fractions (1) , set up to get the final units you want • When you add units (“words”) to fractions, you can treat them just like numbers (1) (1) (1) (1) 20$ x 8 hours x 5 days x 4 weeks x 12 months hour day week month year

7. Calculate • It all boils down to multiplying your starting info by a series of “unity” fractions (1) , set up to get the final units you want • When you add units (“words”) to fractions, you can treat them just like numbers (1) (1) (1) (1) 20$ x 8 hours x 5 days x 4 weeks x 12 months hour day week month year 20 x 8 x 5 x 4 x 12 $ year

8. I’ll take the job! • It all boils down to multiplying your starting info by a series of “unity” fractions (1) , set up to get the final units you want • When you add units (“words”) to fractions, you can treat them just like numbers (1) (1) (1) (1) 20$ x 8 hours x 5 days x 4 weeks x 12 months hour day week month year 20 x 8 x 5 x 4 x 12 $ year $ = 38,400 year

9. I’ll take the job! • It all boils down to multiplying your starting info by a series of “unity” fractions (1) , set up to get the final units you want • When you add units (“words”) to fractions, you can treat them just like numbers (1) (1) (1) (1) 20$ x 8 hours x 5 days x 4 weeks x 12 months hour day week month year 20 x 8 x 5 x 4 x 12 $ year $ = 38,400 year Anyone see the problem?

10. Example: Songs • How many songs are in all the iPods at school? • Start by collecting data • 0.5 iPods/student • 250 songs/iPod • 30 students/classroom • 100 classrooms/school

11. Set up the Fractions 0.5 iPods x 500 songs x 30 students x 100 classrooms student iPod classroom school

12. Cancel Units 0.5 iPods x 500 songs x 30 students x 100 classrooms student iPod classroom school

13. Cancel … 0.5 iPods x 500 songs x 30 students x 100 classrooms student iPod classroom school

14. Keep going… 0.5 iPods x 500 songs x 30 students x 100 classrooms student iPod classroom school

15. Calculate 0.5 iPods x 500 songs x 30 students x 100 classrooms student iPod classroom school 0.5 x 500 x 30 x 100 songs school

16. Answer 0.5 iPods x 500 songs x 30 students x 100 classrooms student iPod classroom school 0.5 x 500 x 30 x 100 songs school = 750,000 songs/school

17. Energy Unit Conversions • Question: How important is each type of energy use in my home? • 10,000 kilowatt-hours (kWh)/year of electricity • 200 thousand cubic feet (ccf) of natural gas • 50 gallons of heating oil • Apples and Oranges -- How can you express these in “common units”??

18. Set up the Fractions Electricity: 10,000 kWh x 3,412 BTU x 1 MMBTU year kWh 1,000,000 BTU

19. Cancel, Multiply --> Answer Electricity: 10,000 kWh x 3,412 BTU x 1 MMBTU year kWh 1,000,000 BTU = 10,000 x 3412 x 1 MBTU Year 1,000,000 = 34.1 MBTU Year

20. Set up the Fractions Natural Gas: 200 ccf x 105,000 BTU x 1 MMBTU year ccf 1,000,000 BTU

21. Cancel, Multiply --> Answer Natural Gas: 200 ccf x 105,000 BTU x 1 MMBTU year ccf 1,000,000 BTU = 200 x 105,000 x 1 MBTU 1,000,000 Year = 21.0 MBTU Year

22. Set up the Fractions Oil: 50 gallons x 138,095 BTU x 1 MMBTU year gallon 1,000,000 BTU

23. Cancel, Multiply --> Answer Oil: 50 gallons x 138,095 BTU x 1 MMBTU year gallon 1,000,000 BTU = 50 x 138,095 x 1 MBTU 1,000,000 Year = 6.9 MBTU Year

24. The Answer Electricity: 34.1 MMBTU/year Natural Gas: 21.0 MMBTU/year Oil: 6.9 MMBTU/year TOTAL:62.0 MMBTU/year