# Presentation: 281271

## 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

**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

- 20_  __$__  _   x   8 _hours_   x    5  _days_   x   4 _weeks_   x   12 _months_

- (1)

- (1)

- (1)

- (1)

## Cancel Units

**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

- 20_  __$__  _   x   8 _hours_   x    5  _days_   x   4 _weeks_   x   12 _months_

- (1)

- (1)

- (1)

- (1)

## Cancel ...

**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

- 20_  __$__  _   x   8 _hours_   x    5  _days_   x   4 _weeks_   x   12 _months_

- (1)

- (1)

- (1)

- (1)

## Cancel ...

**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

- 20_  __$__  _   x   8 _hours_   x    5  _days_   x   4 _weeks_   x   12 _months_

- (1)

- (1)

- (1)

- (1)

## Cancel ...

**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

- 20_  __$__  _   x   8 _hours_   x    5  _days_   x   4 _weeks_   x   12 _months_

- (1)

- (1)

- (1)

- (1)

## 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

- year

- 20         x   8             x    5             x   4              x   12     _$        _

-    hour           day                week         month               year

- 20_  __$__  _   x   8 _hours_   x    5  _days_   x   4 _weeks_   x   12 _months_

- (1)

- (1)

- (1)

- (1)

## I’ll 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

- year

- 20         x   8             x    5             x   4              x   12     _$        _

- = 38,400

- year

- _$_

-    hour           day                week         month               year

- 20_  __$__  _   x   8 _hours_   x    5  _days_   x   4 _weeks_   x   12 _months_

- (1)

- (1)

- (1)

- (1)

## I’ll 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

- year

- 20         x   8             x    5             x   4              x   12     _$        _

- = 38,400

- year

- _$_

-    hour           day                week         month               year

- 20_  __$__  _   x   8 _hours_   x    5  _days_   x   4 _weeks_   x   12 _months_

- (1)

- (1)

- (1)

- (1)

- 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

## Cancel Units

- 0.5   _iPods_    x    500 _songs_   x    30   _students_    x  100 _classrooms_

- student                iPod                classroom                school

## Cancel ...

- 0.5   _iPods_    x    500 _songs_   x    30   _students_    x  100 _classrooms_

- student                iPod                classroom                school

## Keep going...

- 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                x    500              x    30                     x  100  _ __songs_

- school

**=   750,000 ****songs/school**

- 0.5   _iPods_    x    500 _songs_   x    30   _students_    x  100 _classrooms_

- student                iPod                classroom                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”??***

## Set up the Fractions

**Electricity:**  10,000_ kWh_     x     3,412 _ BTU_      x        1     _MMBTU_

-                                year                      kWh         1,000,000  BTU

## 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

## Set up the Fractions

**Natural Gas:**  200 _ ccf_      x  105,000 _ BTU_    x   1      _MMBTU_

-                            year                        ccf              1,000,000  BTU

## 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_

-   Year

- 1,000,000

-                 =         _21.0 _   _MBTU_

-  Year

## Set up the Fractions

**     ****Oil:  **  50  _ gallons_      x  138,095 _BTU_         x     1      _MMBTU_

-                      year                          gallon             1,000,000  BTU

## Cancel, Multiply --> 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

## The Answer

**Electricity:****	****	**34.1 MMBTU/year
**Natural Gas:****	****	**21.0 MMBTU/year**	**
**Oil:****	****	****	****  **_6.9 __MMBTU/year_
**TOTAL:**		**62.0 ****MMBTU/year**