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Learn the rules for counting significant figures and how to apply them in calculations for multiplication, division, addition, and subtraction. Also, understand the rules for rounding off numbers accurately.
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Calculations with Significant Figures • Rules for Counting Significant Figures
Rules for Significant Figures in Calculations • For Multiplication and Division • a. Count the number of significant figures in each measurement • c. Round the result so it has the same number of significant figures as the measurement with the smallest number of significant figures • 4.5 cm x 0.200 cm = 0.90 cm2 • 2 sig figs 3 sig figs 2 sig figs • For Addition and Subtraction • a. Result is limited by the number with the smallest number of significant decimal places • b. Find last significant figure in each measurement • c. Find which one is “left-most” • d. Round answer to the same decimal place • 450 mL + 27.5 mL = 480 mL • precise to 10’s place precise to 0.1’s place precise to 10’s place
Rules for Rounding Off • 1. If the digit to be removed is: • a. < 5, the preceding digit stays the same (1.33 becomes 1.3) • b. ≥ 5, the preceding digit is increased by 1 (1.36 becomes 1.4) • In a series of calculations, carry the extra digits to the final result and then round off. • 1.5 x 2.54 = 3.81 ÷ 2.33 = 1.6351931 Rounds to 1.6 • Don’t forget to add place-holding zeros if necessary to keep value the same!! 3.496 (4 figs) rounds to 3.50 (3 sig figs) not 3.5 (2 sig figs)
I. Density • A. Density is a property of matter representing the mass per unit volume d = m/V • 1. Density can be used to identify unknowns or test for composition • 2. Density : solids > liquids >>> gases • 3. Solids = g/cm3 Liquids = g/ml Gases = g/L • 4. Example 25.00 ml of isopropanol = 19.625 g d = ? • d = 19.624g / 25.00 ml = 0.7850 g/ml • 5. Today: Identify metal based on its density • Measure mass of unknown metal object on balance • “Tare” sets the balance to 0.000 g • Measure mass to 0.001 g • Volume of object by displacement of water in graduated cylinder Vobject = V(water + object) – V(water only) Al = 2.70 g/cm3 Fe = 7.87 g/cm3 Brass = 8.40 g/cm3 Pb = 11.34 g/cm3
Graphing • Circumference = Pi x Diameter (C = pd) (y = mx + b) • Measure C and d for several different sizes of beakers • diameter (cm) circumference (cm) • 10 31 • 20 63 • 30 94 • 40 123 • Manual Graph • Required: Title, Name, Date, Axes Labels with units, • use most of paper • Best fit straight line • Excel Graph on your own • Turn in next week: Data sheets, Excel Graph, Excel spreadsheet
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