Unit Conversions - PowerPoint PPT Presentation

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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 – PowerPoint PPT presentation

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Title: 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 --gt /year
  • Price dollars per pound /lb --gt /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
Ill 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
Ill 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 --gt 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 --gt 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
Year
1,000,000
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 --gt Answer
Oil 50 gallons x 138,095 BTU
x 1 MMBTU
year
gallon 1,000,000 BTU
50 x
138,095 x 1 MBTU
Year
1,000,000
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
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