Dimensional Analysis, Significant Figures, & the Metric System

Accuracy vs. Precision ACCURATE = CORRECT PRECISE = CONSISTENT Accuracy - how close a measurement is to the accepted value Precision - how close a series of measurements are to each other ACCURATE = CORRECT PRECISE = CONSISTENT

Percent Error your value accepted value Indicates accuracy of a measurement your value accepted value

Percent Error Example % error = 2.9 % A student determines the density of a substance to be 1.40 g/mL. Find the % error if the accepted value of the density is 1.36 g/mL. % error = 2.9 %

Significant Figures Indicates precision of a measurement. Counting Sig Figs Count all numbers EXCEPT: Leading zeros -- 0.0025 Trailing zeros without a decimal point -- 2,500

Counting Significant Figures 1. 23.50 1. 23.50 4 sig figs 2. 402 2. 402 3 sig figs 3. 5,280 3. 5,280 3 sig figs 4. 0.080 4. 0.080 2 sig figs

Calculating Significant Figures Multiply/Divide - The # with the fewest sig figs determines the # of sig figs in the answer. (13.91g/cm3)(23.3cm3) = 324.103g 4 SF 3 SF 3 SF 324 g

Calculating Significant Figures (cont’d.) Add/Subtract - The # with the lowest decimal value determines the place of the last sig fig in the answer. 3.75 mL + 4.1 mL 7.85 mL 3.75 mL + 4.1 mL 7.85 mL 224 g + 130 g 354 g 224 g + 130 g 354 g  7.9 mL  350 g

Scientific Notation 65,000 kg  6.5 × 104 kg Converting into Sci. Notation: Move decimal until there’s 1 digit to its left. Places moved = exponent. Large # (>1)  positive exponent (“up”) Small # (<1)  negative exponent (“down”) “If it was left up to me, I would put it right down” Only include sig figs.

Scientific Notation Practice Problems 1. 2,400,000 g 2. 0.00256 kg 3. 7  10-5 km 4. 6.2  104 mm 2.4  106 g 2.56  10-3 kg 0.00007 km 62,000 mm

Proportions Direct Proportion y = x y x Inverse Proportion y = 1 x y x

SI Units Quantity Symbol Base Unit Abbrev Length l meter m Mass m kilogram kg Time t second s Temp T kelvin K Amount n mole mol

SI Units Prefix Symbol Factor mega- M 106 kilo- k 103 BASE UNIT --- 100 deci- d 10-1 centi- c 10-2 milli- m 10-3 micro-  10-6 nano- n 10-9 pico- p 10-12

M V D = Derived Units 1 cm3 = 1 mL 1 dm3 = 1 L Combination of base units Volume (m3 or cm3) length  length  length 1 cm3 = 1 mL 1 dm3 = 1 L D = M V Density (kg/m3 or g/cm3) mass per volume

lecturePLUS Timberlake Density Density compares the mass of an object to its volume D = mass = g or g volume mL cm3 lecturePLUS Timberlake

Dimensional Analysis The “Factor-Label” Method Units, or “labels” are canceled, or “factored” out

Dimensional Analysis Steps: 1. Identify starting & ending units. 2. Line up conversion factors so units cancel. 3. Multiply all top numbers & divide by each bottom number. 4. Check units & answer.

Dimensional Analysis Example You have 1.5 pounds of gold. Find its volume in cm3 if the density of gold is 19.3 g/cm3. lb cm3 1.5 lb 1 kg 2.2 lb 1000 g 1 kg 1 cm3 19.3 g = 35 cm3