27 August Significant Figures (Sig Figs) No ...
27 August
Significant Figures (Sig Figs) No measurement is ever perfect Always a degree of uncertainty Sometimes shown with “±” as in 1.5 ± 0.1 mL If there’s no “±”, uncertainty assumed in the last digit The more digits, the more certain the measurement
Determining Sig Figs #1: all non – zero digits 89.6 µm has 3 sig figs #2: all zeroes between non – zero digits 10,345 lb has 5 sig figs #3: leading zeroes are NOT 0.00035 sec has 2 sig figs #4: ending zeroes depend #4a: no decimal → no 1500 atm has 2 sig figs #4b: between non – zero and decimal on right → yes 300. MHz has 3 sig figs #4c: decimal on left, after non – zero →yes 0.0400 mL has 3 sig figs #5: scientific notation always shows sig figs 20,000 mi looks like 1 sig fig vs. 2.0 x 104 mi shows 2 sig figs 1.2 x 102 vs. 1.20 x 102
Practice How many sig figs?
1. 32.010 a. 3 b. 4 c. 5 * 2. 0.0032 a. 4 b. 2 * c. 5 3. 30.0 a. 1 b. 2 c. 3 * Significant zeroes? 50,400 a. 1 * b. 2 c. 3
Why do we care? Your calculated answer cannot be more certain than your measurements → initial sig figs inform your answer Multiplication and division: the answer must contain the same # of sig figs as that of the LEAST certain number Volume of a cube 3.4 in to a side V = r3 = (3.4 in)3 = 39.304 in3 Must round to 39 in3 12.2 / 3.405 = 3.58297 Must round to 3.58 Addition and subtraction: the answer must contain the same # of decimal places as that with the fewest # of decimal places
900. mL – 48.2 mL = 851.8 mL Round to ones, so 852 mL 0.342 – 0.45 = 0.792 Round to hundredths, so 0.79
Other sig fig issues Pay attention to order of operations 7.87 mL / (16.1 mL – 8.44 mL) 7.87 mL / (7.7 mL) Must round to ones place 1.0 mL Must round to 2 sig figs Exact figures (no uncertainty) do not affect sig figs Volume of a sphere with radius 0.32 in V = 4/3 π r3 V = 4/3 π (0.32)2 V = 0.14 in3 Only 0.32 determines sig figs 4/3 and π are both exact figures
Precision and Accuracy Precision – consistent reproduction, data clustered closely together, reproducible Accuracy – nearness to the actual Do not always occur together
Error Random error – always occurs, tends to make measurements scatter Systematic error - connected to a faulty experiment or the measurer making a consistent mistake, measurements cluster above or below actual, fixable
Practice A bottle has a volume of 2.4 gallons. What is this volume in cm3? 2.4 gal → cm3 1 gal = 3.785 dm3 dm = 10 m cm = 10-2 m 10 cm = 1 dm 2.4 gallons x (3.785 cm3 / 1 gallon) x ((10 cm)3 / (1 dm)3) 9100 cm3
Significant Figures (Sig Figs) No measurement is ever perfect Always a degree of uncertainty Sometimes shown with “±” as in 1.5 ± 0.1 mL If there’s no “±”, uncertainty assumed in the last digit The more digits, the more certain the measurement
Determining Sig Figs #1: all non – zero digits 89.6 µm has 3 sig figs #2: all zeroes between non – zero digits 10,345 lb has 5 sig figs #3: leading zeroes are NOT 0.00035 sec has 2 sig figs #4: ending zeroes depend #4a: no decimal → no 1500 atm has 2 sig figs #4b: between non – zero and decimal on right → yes 300. MHz has 3 sig figs #4c: decimal on left, after non – zero →yes 0.0400 mL has 3 sig figs #5: scientific notation always shows sig figs 20,000 mi looks like 1 sig fig vs. 2.0 x 104 mi shows 2 sig figs 1.2 x 102 vs. 1.20 x 102
Practice How many sig figs?
1. 32.010 a. 3 b. 4 c. 5 * 2. 0.0032 a. 4 b. 2 * c. 5 3. 30.0 a. 1 b. 2 c. 3 * Significant zeroes? 50,400 a. 1 * b. 2 c. 3
Why do we care? Your calculated answer cannot be more certain than your measurements → initial sig figs inform your answer Multiplication and division: the answer must contain the same # of sig figs as that of the LEAST certain number Volume of a cube 3.4 in to a side V = r3 = (3.4 in)3 = 39.304 in3 Must round to 39 in3 12.2 / 3.405 = 3.58297 Must round to 3.58 Addition and subtraction: the answer must contain the same # of decimal places as that with the fewest # of decimal places
900. mL – 48.2 mL = 851.8 mL Round to ones, so 852 mL 0.342 – 0.45 = 0.792 Round to hundredths, so 0.79
Other sig fig issues Pay attention to order of operations 7.87 mL / (16.1 mL – 8.44 mL) 7.87 mL / (7.7 mL) Must round to ones place 1.0 mL Must round to 2 sig figs Exact figures (no uncertainty) do not affect sig figs Volume of a sphere with radius 0.32 in V = 4/3 π r3 V = 4/3 π (0.32)2 V = 0.14 in3 Only 0.32 determines sig figs 4/3 and π are both exact figures
Precision and Accuracy Precision – consistent reproduction, data clustered closely together, reproducible Accuracy – nearness to the actual Do not always occur together
Error Random error – always occurs, tends to make measurements scatter Systematic error - connected to a faulty experiment or the measurer making a consistent mistake, measurements cluster above or below actual, fixable
Practice A bottle has a volume of 2.4 gallons. What is this volume in cm3? 2.4 gal → cm3 1 gal = 3.785 dm3 dm = 10 m cm = 10-2 m 10 cm = 1 dm 2.4 gallons x (3.785 cm3 / 1 gallon) x ((10 cm)3 / (1 dm)3) 9100 cm3
