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