Expressing Measurements Scientific notation A number is written as the product of two numbers A coefficient 10 raised to a power Example: Put IN Scientific Notation A. 602,000,000 B. 0.00774560 C. 2.753 6.02x108 7.74560 x10-3 2.753 x100

Expressing Measurements Example: Put OUT of Scientific Notation A. 3.51 x104 B. 5.001 x10-5 35,100 .00005001 Example: Put in CORRECT Scientific Notation A. 237.1 x103 B. 43578.1 x10-5 2.317 x105 4.35781 x10-1

Scientific Measurement Measurement depends on Accuracy (“Correctness”) A measure of how close a measurement comes to the actual or true value of whatever is measured Precision (“Reproducibility”) A measure of how close a series of measurements are to one another Examples:

Scientific Measurement Measurement is never certain because measurement instruments are never free of flaws. So we only count numbers that are SIGNIFICANT ***All certain numbers plus one uncertain number***

Rules for Counting SIG FIGS NON ZERO INTERGERS: are ALWAYS significant Examples: 352.1 mL = _____ sig figs 62 in. = _____ sig figs 43,978.6821g = _____ sig figs

Rules for Counting SIG FIGS 2. ZEROS (There are three classes) LEADING ZEROS are NEVER significant Examples: .034 g = _____ sig figs 0.0006178 m = _____ sig figs

Rules for Counting SIG FIGS B. CAPTIVE ZEROS are ALWAYS significant Examples: 205 mi = _____ sig figs 10,005 g = _____ sig figs

Rules for Counting SIG FIGS C. TRAILING ZEROS are SOMETIMES significant. Only when there is a decimal point* Examples: 16,000 mi = _____ sig figs 16,000.0 mi = _____ sig figs 2.3500 m = _____ sig figs

Rules for Counting SIG FIGS 3. EXACT NUMBERS are INFINATELY significant Examples: Counting students Conversions

OPERATIONS & SIG FIGS “The result of calculations involving measurements can only be as precise as the least precise measurement”

OPERATIONS & SIG FIGS 1. MULTIPLICATION AND DIVISION The product (x) or quotient (/) contain the same number of sig figs as the measurement with the least number of sig figs. Example: 24 cm x 31.8 cm = 763.2 cm2  760 cm2

OPERATIONS & SIG FIGS 2. ADDITION AND SUBTRACTION The sum or difference has the same number of decimal places as the number with the least decimal places. Examples: 7.52 cm + 8.7 cm = 16.22 cm  16.2 cm 39 m + 0.7893 m = 39.7893 m  40. m

Metric System History – people did not have measuring devices readily available English (customary units) Foot = length of king’s foot at the time Inch = length between 1st & 2nd knuckles Pound (lb) = “Liberty” or “Justice” used to measure grains Metric Meter – originally 1/10,000,000 of distance from North Pole to equator Gram – weight of 1 cm3 block and 1cc of H2O in syringe Liter = 1,000 cm3

SI Units Treaty in 1875 to come up with standard system Basic SI Units International System of Measurements (SI) French: Le Système international d'unités Basic SI Units Length = meter (m) Mass = kilogram (kg); gram is too small to use as basic unit Time = seconds (s) Electric current = ampere (amp) Temperature = Kelvin (K); never use °K; based on absolute zero Amount of a substance = mole (mol) Luminous intensity = candela All other units are derived from these 7 basic units

Area = l × w = m × m Denisty = mass/volume = kg/l × w × h (m × m × m) psi = lb/in2  kg/m

Metric Prefixes (example: density kg/m3) Basic Units Mass = gram (g) Length = meter (m) Volume = liter (L) There are three major parts to the metric system: the seven base units (example: meters) the prefixes (example: kilometer) units built up from the base units. (example: density kg/m3)

Prefix Symbol Numerical Exponential tera T 1,000,000,000,000 1012 giga G 1,000,000,000 109 mega M 1,000,000 106 kilo k 1,000 103 hecto h 100 102 Deka da 10 101 Unit No prefix (m, L, g) 1 100

Prefix Symbol Numerical Exponential deci d 0.1 10-1 centi c 0.01 10-2 milli m 0.001 10-3 micro  0.000001 10-6 nano n 0.000000001 10-9 pico p 0.000000000001 10-12

Putting it All Together 1 kilometer = 1 x 103 m = 1000 m 1 picometer = 1 x 10-12 m = 0.000000000001 m 1 milligram = 1 x 10-3 g = 0.001 g

Need to know all the units, especially k h d u d c m Note: There are units between these numbers (i.e., 10-4, 10-5, etc.) but they don’t have a prefix, so we don’t discuss them Need to know all the units, especially k h d u d c m “King Henry drinks up delicious chocolate milk.”

Metric Conversions memorize the metric prefixes names and symbols. determine which of two prefixes represents a larger amount. determine the exponential "distance" between two prefixes.

Practice! 22.6 mm = _______ m .61 gh = _____ cg 78.5 mL = _____ L Answer: 0.0226 m (already in correct # of sig figs) .61 gh = _____ cg Answer: 6100 cg 78.5 mL = _____ L Answer: 0.0785 L

Memorize These!!! 1 L = 1 dm3 1 mL = 1 cm3 dm3 used for solid volume; L or mL used for liquid volume 1 mL = 1 cm3 1 mL of H2O = 1 g = 1 cm3 (a.k.a., “cc” in hospitals)

These are Tricky Ones Whenever you see squares or cubes, slow down and handle the problem differently 12.0 cm2 = _____ mm2 Answer: 1200 mm2 21 mL = _____ cm3 Answer: 21 cm3

Just for Fun 5.82 mm = ______ Tm 35.2 dm2 = _____ hm2 2.79 L = _____dm3 45 km/min = _____ m/s Hardest one I can give you (no setup = no credit): 3 weeks = _____ s