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Corresponds to “Chapter 3” & “Appendix C: Math Handbook” (pgs R56-63). Scientific Measurement. Using and Expressing Measurements. Measurement A quantity that has both a NUMBER and a UNIT Units are metric* Scientific Notation Product of a coefficient and 10 raised to a power
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Corresponds to “Chapter 3” & “Appendix C: Math Handbook” (pgs R56-63) Scientific Measurement
Using and Expressing Measurements • Measurement • A quantity that has both a NUMBER and a UNIT • Units are metric* • Scientific Notation • Product of a coefficient and 10 raised to a power • Coefficient must be 1 ≤ # ≥ 9 • 100 = 1 • 101 = 10 • Use “EE” or “EXP” or “E” button • means “times 10 to the”
Accuracy, Precision, and … • Accuracy • Measure of how close a measurement comes to the actual or true vale of whatever is measured • How close to the bulls-eye did your dart(s) land? • Precision • Measure of how close a series of measurements are to one another • How close together are all your darts? (regardless of proximity to bulls-eye)
And …. Error • Error = experimental value – accepted value • Exp value = measured in lab • Accepted value = correct value based on reliable references or formulas • % error = l error l x 100 % accepted • % error = (the absolute value of exp – accepted) divided by the accepted value, times 100 to make it a %
Significant Figures • ALL “known” digits + 1 “estimated” digit • Known are digits clearly marked by instrument increments • Estimated is the smallest increment divided by 10 • So if ruler marks off millimeters (0.001 m) then the unknown digit will be the ten-thousandths’ place (0.0001 m)… or 0.1 mm • Sig figs can be annoying, but it is important to only record measurements to the most or least precise it can be… • Think adding exactly 1.00mL from an eye-dropper to a gallon of fluid… why bother taking the time to be perfect with the 1.00mL?
Rules … you’re given a measurement, are the digits sig? • All nonzero digits are significant • 1998 m = 4 sig figs • Embedded zeros are significant • 2002 L = 4 sig figs • Leading zeros are NOT significant • 0.08 g = 1 sig fig • (because could be written as 8 X 10-2 g…clearly 1 sig fig) • Trailing zeros are NOT sig, UNLESS a decimal point is involved • 2010 mg = 3 sig figs, BUT 201.0 cg = 4 sig figs; • 2010. mg = 4 sig figs • although that format is frowned upon because it could and should be written as 2.010 x 103 mg (obviously 4 sig figs still)
Unlimited number of sig figs? Woohoo! • Counted numbers • 24 students in the classroom • 5 “digits” on my hand • Defined quantities • 60 minutes = 1 hour • 100 pennies = 1 dollar • 100 cm = 1 m
Rounding- you’re not in math class anymore… • If digit ≤4, truncate (drop) • 2.22 cm 2.2 cm • If digit > 5, round up • 1.68 cm 1.7 cm • If digit = 5, look at numbers after OR before • If there is a NONZERO digit AFTER a 5, round the 5 up (ex: 1.251 cm 1.3 cm) • If there is a ZERO or NO DIGIT after a 5, look at the digit BEFORE • If digit is EVEN, truncate 5 (ex: 1.250 cm 1.2 cm) • If digit is ODD, round up (ex: 1.15 cm 1.2 cm)
Sig Figs in calculations = more rules • A calculated answer can NEVER be more precise than the least precise measurement from which it is calculated • Think eye-dropper into gallon again • Think “a chain is only as strong as its weakest link” • Addition & Subtraction • Keep the LEAST number of DECIMAL PLACES • 1.8 mL + 2 mL = 3.8 mL 4 mL (must round to “ones”) • Multiplication & Division • Keep the LEAST number of SIGNIFICANT FIGURES • 1.8 m X 2.71 m = 4.878 m2 4.9 m2 (must round to 2 figures) • Yes, PEMDAS is still in effect
Metric (goes hand-in-hand with SI: The International System of Units) • Based on powers of 10 • Common units [with prefixes if needed] • Meter (length) • Gram (mass) • Second (time) • Liter (volume) • If measuring a large item, use a larger unit • If measuring tiny item, use a smaller unit
Conversion Factors • Used to convert the same quantity of something to a new unit • Ex: 1 mL = 1 cm3 (or 1 cc)
