Last time… Fundamental SI units Length (meter), time (second), mass (kilogram) “mks” system (metric system) Unit conversion “unit conversion ratio” All units cancel out except the one to which we’re converting Compound quantities and compound units Build new units from the three SI units Dimensional analysis Determine the “properties” of an equation by identifying its units

Order of Magnitude Estimation

The Size of Things How big is big, how small is small? Typical person: –Adult size: m tall –Adult mass: kg –Lifespan: 80 years = s Typical housefly: –Adult size: 5-7 mm = m –Adult mass: 12 mg = kg –Lifespan: 7 days = s

Orders of Magnitude We can do a quick comparison by considering the order of magnitude of the measurement Typical person: –Adult size = m  1 m –Adult mass = kg  100 kg –Lifespan = s  1,000,000,000 s Typical housefly: –Adult size – m  0.01 m –Adult mass = kg  kg –Lifespan = s  s

Scientific Notation The key to working with orders of magnitude is scientific notation Typical person: –Adult size  1 m = 10 0 m –Adult mass  100 kg = 10 2 kg –Lifespan  1,000,000,000 s = 10 9 s Typical housefly: –Adult size  0.01 m = m –Adult mass  kg = kg –Lifespan  1,000,000 s = 10 6 s People live about 10 3 = 1000 times longer. People are about 10 7 = 10 million times as massive People are about 10 2 = 100 times taller than flies.

Orders of magnitude (length scale) ObjectSize Universe10 23 m Solar System10 10 m Earth10 6 m Football field10 2 m You10 0 m Germ10 -6 m Atom m Proton m SAT Flashback! The length scale of the universe is to the length scale of the earth as the length scale of a football field is to the length scale of _______.

Orders of magnitude and SI prefixes ObjectSize Giga (G)10 9 mega (M)10 6 kilo (k) centi (c)10 -2 milli (m)10 -3 Micro (  ) Nano (n)10 -9 How many millimeters are in one kilometer? 1 km = 10 3 m 1 mm = m So, 1 km = 10 6 mm

Summary of Estimation Techniques How “exact” do calculations have to be? Sometimes we only have to know the order of magnitude of a value to make an educated guess! ESTIMATION = BALL-PARK FIGURE Use usual rounding techniques: e.g ~ 10 3 but 6782 ~ 10 4 Always make sure you compare values that have the same units! Use the information at your disposal first; then if you can find it, look it up!