Metrics and Dimensional Analysis

1. Chem and Society Fall 2006 Paris Hilton loves it, so should you! Metrics and Dimensional Analysis

2. UNITS OF MEASUREMENT • English • Weight: ounce, pound, ton • Length: inch, foot, yard, mile • Volume: cup, pint, quart, gallon • Not used in science

3. Confusing and difficult to keep track of conversions

4. METRIC SYSTEM • Metric system (Le Systeme International d’ Unites) AKA “S.I.”– common units of measurement for everyone (else) • Based on multiples or divisions of base unit 10 (remember the Dewey decimal system?) • Common metric units of measure for: • Length: meter • Mass: gram • Volume: Liter • Time: second • Energy: Joule • Temperature: Celsius or Kelvin

5. Dimensional Analysis Dimensional Analysis is not for everyone. But it's probably for you. First of all then, who should avoid Dimensional Analysis (DA)? Reasons for not using Dimensional Analysis 1. Let's say you're super-intelligent and enjoy solving relatively simple problems in the most complex manner. 2. Let's say you're tired of always getting the correct answers. 3. Let's say you're an arty type and you can't be confined by the structure of DA. You like messy solutions scribbled all over the page in every which direction. It's not that you want to make a mistake. But you really don't care that much about the answer. You just like the abstract design created by the free-wheeling solution... and the freedom from being confined by structure. 4. Let's say that you have no interest in going to the prom or making the soccer team, and you don't mind being unpopular, unattractive, ignorant, insecure, uninformed, and unpleasant.

6. You NeedDimensional Analysis! Testimonials "I was a Fairborn High School student who dozed off while Mrs. Lehner taught us dimensional analysis in chemistry. I never quite got the hang of it. It irritated me... all of those fractions. I never really liked fractions. Although my grades had been pretty high, I got a D in chemistry and subsequently dropped out in the first quarter of my junior year. It was not long before I started on drugs, and then crime to support my drug habit. I have recently learned dimensional analysis and realize how simply it could have solved all of my problems. Alas, it is too late. I won't get out of prison until 2008 and even then, my self image is permanently damaged. I attribute all of my problems to my unwillingness to learn dimensional analysis." -Jane "I thought I knew everything and that sports was the only thing that mattered in high school. When Mr. McCollum taught our class dimensional analysis, I didn't care about it at all. I was making plans for the weekend with my girlfriend who loved me because I was a running back and not because of chemistry. While other kids were home solving dimensional analysis problems, I was practicing making end sweeps. Then one day I was hit hard. Splat. My knee was gone. I was despondent. My girl friend deserted me. My parents, who used to brag about my football stats, started getting on my case about grades. I decided to throw myself into my school work. But I couldn't understand anything. I would get wrong answers all of the time. I now realize that my failure in school came from never having learned dimensional analysis. Alas, I thought everyone else was smarter. After the constant humiliation of failing I finally gave up. I am worthless. I have no friends, no skills, no interests. I have now learned dimensional analysis, but it is too late." - Bill

7. The evidence: Studies in Fairborn High School from 1994-99 show that 100% of high school students who do not use and understand dimensional analysis are seriously insecure by their junior year. Damage done from this deprivation in the first two years of high school is probably permanent and cannot be overcome by learning the method later in life. We recommend mastering this skill before your junior year. 83% of the students who went to the senior proms from 1994-99 admitted that they enjoyed solving problems with Dimensional Analysis in order to impress and confuse their parents. Of the remaining 17%, 11% were home from the senior prom before 11 PM and 7 % went home alone. The following testimonial was recently supplied by Mr. Kirk. I see no reason to doubt the validity of this testimonial, however I should add that I have no direct knowledge whatever of Mario. I was at home, sick with the flu when Mr. Kirk taught my class about Dimensional Analysis. Despite opportunities given to me to make up the assignments that I had missed, I chose to not do them. I thought that my mathematical abilities were already sufficient. How wrong I was! It’s been five years since I took that class--Now I spend my afternoons panhandling at traffic lights, hoping for passersby to give me spare change. If I ‘m lucky enough to scam a buck after a day’s work, I’m still not sure if my hourly rate makes cents. --Mario

8. What's the method? Example 1 Example 2 This is a structured way of helping you to convert units. With this method, you can easily and automatically convert very complex units if you have the conversion formulas. The method involves the following steps Convert 6.0 cm to km Convert 4.17 kg/m2 to g/cm2 1. Write the term to be converted, (both number and unit) 6.0 cm 4.17 kgm2 2. Write the conversion formula(s) 100 cm = .00100 km 1.00 m = 100 cm 1.00 kg = 1000 g 3. Make a fraction of the conversion formula, such that a) if the unit in step 1 is in the numerator, that same unit in step 3 must be in the denominator. b) if the unit in step 1 is in the denominator, that same unit in step 3 must be in the numerator. Since the numerator and denominator are equal, the fraction must equal 1. .00100 km100 cm 1000 g 1.00 m 1.00 m1.00 kg 100 cm 100 cm 4. Multiply the term in step 1 by the fraction in step 3. Since the fraction equals 1, you can multiply by it without changing the size of the term. 6.0 cm.00100 km100 cm 4.17 kg 1000 g 1.00 m1.00 mm2 1.00 kg 100 cm 100 cm 5. Cancel units 6.0 cm .00100 km100 cm 4.17 kg1000 g 1.00 mx1.00 mm2 1.00 kg 100 cm 100 cm 6. Perform the indicated calculation rounding the answer to the correct number of significant figures. .000060 km or 6.0 E -5 km .417 gcm2

9. Example 1 Continued Convert 6.0 cm to km Example 2 Continued Convert 4.17 kg/m2 to g/cm2 4. Multiply the term in step 1 by the fraction in step 3. Since the fraction equals 1, you can multiply by it without changing the size of the term. 6.0 cm x .00100 km1 100 cm 4.17 kg x 1000 g x 1.00 m x 1.00 mm2 1.00 kg 100 cm 100 cm 5. Cancel units 6.0 cm x .00100 km1 100 cm 4.17 kg x 1000 g x 1.00 m x 1.00 mm2 1.00 kg 100 cm 100 cm 6. Perform the indicated calculation rounding the answer to the correct number of significant figures. .000060 km or 6.0 E –5 km .417 gcm2

10. METRIC PREFIXES

11. Metric Prefixes 106 105 104 103 102 101 100 10-1 10-2 10-3 10-4 10-5 10-6 Kilo Base unit deci Hecto milli centi Deka Mega micro Meter Liter gram “King Henry Doesn’t bother drinking chocolate milk” …or whatever works for you 

12. Practice