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# Unit Conversions - PowerPoint PPT Presentation

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]

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• 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]

• 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

• 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

• 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

• 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

• 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

• 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

• 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

• 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?

• 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

0.5 iPods x 500 songs x 30 students x 100 classrooms

student iPod classroom school

0.5 iPods x 500 songs x 30 students x 100 classrooms

student iPod classroom school

0.5 iPods x 500 songs x 30 students x 100 classrooms

student iPod classroom school

0.5 iPods x 500 songs x 30 students x 100 classrooms

student iPod classroom school

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

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

• 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”??

Electricity: 10,000 kWh x 3,412 BTU x 1 MMBTU

year kWh 1,000,000 BTU

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

Natural Gas: 200 ccf x 105,000 BTU x 1 MMBTU

year ccf 1,000,000 BTU

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

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

Electricity: 34.1 MMBTU/year

Natural Gas: 21.0 MMBTU/year

Oil: 6.9 MMBTU/year

TOTAL:62.0 MMBTU/year