Title: Unit Conversions
1Unit 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
2Example 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
3Cancel 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
4Cancel
- 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
5Cancel
- 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
6Cancel
- 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
7Calculate
- 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
8Ill 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
9Ill 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?
10Example 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
11Set up the Fractions
0.5 iPods x 500 songs x 30
students x 100 classrooms
student iPod
classroom school
12Cancel Units
0.5 iPods x 500 songs x 30
students x 100 classrooms
student iPod
classroom school
13Cancel
0.5 iPods x 500 songs x 30
students x 100 classrooms
student iPod
classroom school
14Keep going
0.5 iPods x 500 songs x 30
students x 100 classrooms
student iPod
classroom school
15Calculate
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
16Answer
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
17Energy 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??
18Set up the Fractions
Electricity 10,000 kWh x 3,412 BTU
x 1 MMBTU
year
kWh 1,000,000 BTU
19Cancel, 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
20Set up the Fractions
Natural Gas 200 ccf x 105,000 BTU x
1 MMBTU
year
ccf 1,000,000 BTU
21Cancel, 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
22Set up the Fractions
Oil 50 gallons x 138,095 BTU
x 1 MMBTU
year
gallon 1,000,000 BTU
23Cancel, 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
24The Answer
Electricity 34.1 MMBTU/year Natural Gas 21.0
MMBTU/year Oil 6.9 MMBTU/year TOTAL 62.0
MMBTU/year