1. How to Change Units using Math
DIMENSIONAL ANALYSIS
How to Change Units using Math

2. FRUIT DRINKS
If these are one quart each, how many gallons are here?

3. Dry Quart vs. Liquid Quart
Strawberries and other fruits are often sold in one quart containers. Are these quarts the same size as a quart of strawberry juice?
Dry Quart vs. Liquid Quart
Dry Quart = 1.07 Liquid Quarts

4. What does 8 quarts of strawberries make?
1 PECK

5. Apothecary System used in medicine
Based on the weight of one grain of wheat.
20 grains make a scruple
3 scruples make a dram
8 drams make a ounce
12 ounces make a pound (troy pound)
Does this system of constantly changing numbers make sense?

6. Lets Look at another - Units of Length
12 inches (in)= 1 foot (ft)
3 feet= 1 yard (yd)
16-1/2 feet= 1 rod (rd), pole, or perch, depending on where you are from
40 rods= 1 furlong (fur) = 660 feet
8 furlongs= 1 U.S. statute mile (mi)
1 U.S. statute mile (mi) = 5280 feet
feet  = 1 nautical mile

7. Even More????? 14 pounds= 1 stone 2 stones= 1 quarter = 28 pounds
4 quarters= 1 hundredweight = 112 pounds
20 hundredweight= 1 Long Ton = 2240 pounds

8. No, Not MORE 4 gills= 1 pint 2 pints= 1 quart 4 quart= 1 gallon
2 gallons= 1 peck
8 gallons (4 pecks)= 1 bushel
8 bushels= 1 quarter

9. AND THIS IS THE SYSTEM Americans say it easy????????????????
How about the Metric System, it is based only on 10

10. Why Do Units Matter? Why is it Important to always write the Units?
I know what the answer should be in, why do I have to write the stupid unit?

11. MARS CLIMATE ORBITER

13. Dec. 11, 1998

14. The loss of the the Mars Climate Orbiter on September 23, 1999, was a most unfortunate and highly avoidable event.
The cause of the mishap has been traced to a mix-up over units. Preliminary findings indicated that one team used English units (e.g., inches, feet and pounds) while the other used metric units for maneuvers required to place the spacecraft in the proper Mars orbit.
The 'root cause' of the loss of the spacecraft was the failed translation of English units into metric units.
For nearly three centuries, engineers and scientists have been struggling with English units.

15. Air conditioner rated at 18,000 BTU per hour.
What does BTU stand for and what does it measure?
British Thermal Units = Energy to raise or lower 1 pound of water 1 degree Fahrenheit

16. Seabiscuit’s races like most horse races goes for 10 furlongs
Seabiscuit’s races like most horse races goes for 10 furlongs. How far is that?
1 furlong = 1/8 mile

17. In his first annual message to Congress (1790 January), President George Washington pressed for uniformity in currency, weights, and measures. Secretary of State Thomas Jefferson urged Congress to reduce the existing separate systems of dry and liquid measures to one set of measures.
Jefferson
Washington
Over 200 years later, we still have separate systems. For example, our dry quart is larger than our liquid quart, so four cups of flour and 4 cups of milk should be measured with separate measuring devices-which differ in size!
Jefferson's second plan put before Congress was to reduce every branch [of measurement] to the same decimal ratio already established for coin, and thus bring the calculations of the principal affairs of life within the arithmetic of every man who can multiply and divide plain numbers.
Congress took no action.  Washington urged action again in his second annual message to Congress (1790 December 08) and the House referred the matter to the Senate, whose committee in this matter declined (1791 March 01) due to negotiations in progress with the French and British Governments to obtain an international standards of measurements.

18. Currency is based on 10.

19. In the same year of 1790 King Louis XVI of France was also weary of the inconsistencies of measurement that was hurting trade.
He ordered a new system of measurements be developed.

20. Earlier in that century, Fahrenheit and Celsius used water as the basis of their thermometers. Their thermometers were calibrated using water, which everyone had access to. This made their thermometers useful.
Celsius
Fahrenheit

21. Everyone has access to the Earth, so this new system was to be based on the size of the Earth.
The idea was to measure a part of Earth’s surface over a few degrees, then calculate distance from Equator to North Pole.

22. By dividing the distance from the equator to the north pole by 10 million, a convenient length was defined.
Meter
Equator to North Pole
10,000,000
It was a little longer than a yard, and the name would be from the Greek word, Metron, meaning to measure.

23. The motto for the metric system was:
“For all people, for all time”

24. Since we have 10 fingers, a number system based on 10 was developed.

25. 4/20/01
0.5 versus 5

27. DON’T BE A BABY KILLER
If there is no number in front of a decimal point, you MUST put a ZERO (0)
If you have .25 grams as an answer, you must write it 0.25 grams.
Never leave a decimal by itself, they will wonder off and get lost.

28. METER Cubits Yards Miles Nautical Miles Feet Hands Inches Leagues
Chains
Furlongs
METER

29. SI BASE UNITS QUANTITY NAME SYMBOL Length Meter m Volume Liter l
Mass Kilogram Kg
gram g
Time second s
Temperature Kelvin K
Celsius C
Amount mole mol
Memory byte b

30. SI System Prefixes pico- p 10-12 1/1,000,000,000,000
nano- n /1,000,000,000
micro- µ /1,000,000
milli- m /1000
centi- c /100
Kilo- K
Mega- M ,000,000
Giga- G ,000,000,000
Tetra- T ,000,000,000,000
Know these prefixes

31. PUTTING THEM TOGETHER 1000 meters 1 Kilometer
1,000,000 bytes 1 Megabyte
1/1000 Liter 1 milliliter
1/100 meter 1 centimeter
1,000,000,000 seconds 1 Gigasecond

32. Conversion Fractions
A Conversion Fraction is a Fraction that has the units in it and is equal to one
1000m/1Km
100cm/1m
1000mm/1m
1000g/1Kg
NOTE: The larger number always goes with the smaller unit

33. Convert 0.15 meters to centimeters
Starting amount
equal
End Amount
0.15 meters
1 centi
= centimeters
.01
0.15 meters = meters
= 15 centimeters
100
If saying 15 hundredths, just say 15 centi-

34. Convert 5234 millimeters to meters
Starting amount
equal
End Amount
5234 millimeters
0.001
= meters
milli
5234 millimeters meters
1000

35. Convert 5234 millimeters to centimeters
Starting amount
equal
equal
End Amount
5234 millimeters
0.001
centi
= centimeters
milli
0.01
5234. millimeters
523.4 centimeters

36. Convert 5234 millimeters to inches
Units match
Starting amount
equal
equal
End Amount
2.54 cm 1 inch
1 inch 2.54 cm
5234 millimeters
0.001
centi
= inches
milli
0.01

37. Lets try something How many millimeters are in 5 meters
5 m x 1000mm/1m = 5000mm
Let’s look at this:
We write our starting point first, and then determine the fraction, there are 1000 milli’s in one whole, so the fraction is 1000 mm/1 m

38. Let’s try another How many Kilometers are there in 5000 millimeters?
First, remove the starting prefix
5000mm x 1m/1000mm = 5 m
Second, place the new prefix
5 m x 1Km/1000m = Km

39. Let’s Try Another How many milligrams are in 5000 Kilograms?
First, remove the starting prefix:
5000 Kg x 1000g/1Kg = 5000 g
Second, place the ending prefix:
5000g x 1000 mg/1g = 5,000,000 mg

40. LET’S LOOK AGAIN
How many meters will a car traveling 100 Km/hr travel in 1 minute?
This one is a little harder: You have to make two sets of conversions
First Convert 100 Km/hr to meters per hour
100 Km/hr x 1000m/1 Km = m/hr
Second you have to convert m/hr to m/min
m/hr x 1hr/60 min = m/min
Notice: hr goes on top in the conversion because it is on the bottom in the initial number

41. Some Practice Problems
I drive 5 miles to school each morning. How many inches is that? Express your answer in scientific notation.

42. Another one
We have seven class periods here at AHS. If you zone out 5 minutes every class period, how many hours of education will you have missed in the 180-day school year?

43. Again
If a car is traveling 60 miles per hour, how many inches per second is it moving?

44. And Yet Again
Mr Simms wants to give all of his chemistry students enough chocolate to make them goofy for the rest of the day. It's a known fact that it takes 47 chocolate chips to make a student goofy. The average cookie contains 29 chocolate chips. Mr Simms has 5 classes and each class has an average of 32 students. How many toll house cookies does Mr Simms need to make?

45. One Last One
If you never learn dimensional analysis, you will have to work at a fast food restaurant for the rest of your life wrapping hamburgers. Each hour you wrap 184 hamburgers. You work 8 hours per day and work 5 days a week. You get paid every 2 weeks with a salary of $ How many hamburgers will you have to wrap to make your first one million dollars?