1. Dimensional Analysis -Blake Schmidt

2. In science, numbers have meaning…we need UNITS! e.g. If I ask you to measure the length of the lab bench, and you do so and reply 9.3, you really haven’t told me anything. 9.3 what? Lacks dimension. We need UNITS! Units are defined by convention (agreement by many) and related to some standard (at least good ones are). e.g. from knuckle to end of thumb = 1 inch king’s thumb 1/12 th of one foot or 1/36 th of one yard

3. Louis XVI commissioned experts to end confusion Lavoisier and others produced metric system International System of Units (SI) Lots of agreement: exceptions US, Liberia, Burma Powers of 10 simplicity instead of divisibility (1/12 or 1/32) System of prefixes with base unit: e.g. Length: base unit = meter (m) Kilometer (km) = 1000. m

4. 10 24 yotta Y 10 21 zetta Z 10 18 exa E 10 15 peta P 10 12 tera T 10 9 giga G 10 6 mega M 10 3 kilo k 10 2 hecto h 10 1 deka da 10 -1 deci d 10 -2 centi c 10 -3 milli m 10 -6 micro µ 10 -9 nano n 10 -12 pico p 10 -15 femto f 10 -18 atto a 10 -21 zepto z 10 -24 yocto y 10 24 yotta Y 10 21 zetta Z 10 18 exa E 10 15 peta P 10 12 tera T 10 9 giga G 10 6 mega M 10 3 kilo k * 10 2 hecto h 10 1 deka da 10 -1 deci d 10 -2 centi c * 10 -3 milli m * 10 -6 micro µ 10 -9 nano n 10 -12 pico p 10 -15 femto f 10 -18 atto a 10 -21 zepto z 10 -24 yocto y

5. Kilo- = 1000 X base1 km = 1000 m Centi- = 1/100 th X base100 cm = 1 m Milli- = 1/1000 th X base1000 mm = 1 m Therefore, 1 000 000 mm = 1 km

6. Method for converting from one unit to another. Based on conversion factors (essentially multiplying by 1) *no change in meaning How many inches are in 3 feet? 3 ft X = 36 in! Feet cancel: Solve 5x = 10 12 in 1 ft

7. Many of you just did the proportion in your head! G4U! e.g. How many cm in 3.27 miles? Need system to set up conversion factors: dimensional analysis Begin with given: multiply by known conversion factors until desired unit is attained *Remember conversion factors are like multiplying by 1

8. Set up conversions factors as fractions so that units cancel out. e.g. 1 ft x 1 ft = 1 sq ft or 1 ft 2 Multiplied dimensions No canceling out Need to divide by dimension to cancel it out. 1 in or 2.54 cm3 in x 2.54cm = 7.62 cm 2.54 cm 1 in1 in 3 in x 1 in = 1.18 in 2 /cm 2.54 cm

9. How many cm in exactly half a yard? 0.5 yds x 3 ft x 12 in x 2.54 cm = 1 yd 1 ft 1 in 0.5 yds x 3 ft x 12 in x 2.54 cm = 45.72 cm 1 yd 1 ft 1 in

10. Practice How many cm in 1.34 m? Start with given, multiply by appropriate conversion factors to cancel units until you get desired units. 1.34 m x 100 cm = 134 cm 1 m

11. Practice How many km in 1.5E6 cm? 1.5E6 cm x 1 m x 1 km = 15 km 100 cm 1000 m

12. Practice How many m in 250 ft? 250 ft x 12 in x 2.54 cm x 1 m = 76 m 1 ft 1 in 100 cm 250 ft12 in2.54 cm1 m 1 ft1 in100 cm = 76 m

13. Practice The moon is 385 000 km from earth. If the space shuttle travels at 16 500 miles per hour, how many days will it take the shuttle to reach the moon? (1 mi = 1.609 km) 385 000 km1 mi1 hr1 day 1.609 km16 500 mi24 hr = 0.604 days

14. Practice A street-legal, 50 state emission compliant production car is being made in Sweden. The car has reached a top speed of 388 km per hour. How many feet per second does this car travel at top speed? 388 km1 mi5280 ft1 hr1 min 1 hr1.609 km1 mi60 min60 sec = 354 ft/sec

15. Practice How many kL in a cube that measures 1000mm X 100 cm X 1 m? (1 mL = 1 cm 3 1 m 3 100 3 cm 3 1 mL1 L1 kL 1 m 3 1 cm 3 1000 mL1000 L = 1 kL