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## Unit Conversions

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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]

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

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

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

Cancel …

- 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

Cancel …

- 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

Calculate

- 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

I’ll take the job!

- 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

I’ll take the job!

- 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?

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

Set up the Fractions

0.5 iPods x 500 songs x 30 students x 100 classrooms

student iPod classroom school

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

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

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”??

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

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

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

The Answer

Electricity: 34.1 MMBTU/year

Natural Gas: 21.0 MMBTU/year

Oil: 6.9 MMBTU/year

TOTAL:62.0 MMBTU/year

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