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Chapter 3 Measurement Accuracy vs Precision Percent Error Significant Figures Scientific Notation Temperature Conversions Dimensional Analysis Conversion Factors SI Conversions

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Number vs. Quantity Quantity - number + unit UNITS MATTER!!

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A. Accuracy vs. Precision 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

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A. Accuracy vs. Precision

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B. Percent Error Indicates accuracy of a measurement your value given value

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B. Percent Error 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 = 2.94 %

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C. Significant Figures Indicate precision of a measurement. Recording Sig Figs – Sig figs in a measurement include the known digits plus a final estimated digit 2.31 cm

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C. Significant Figures Counting Sig Figs – Digits from 1-9 are always significant – Zeros between two other sig figs are always significant – One or more additional zeros to the right of both the decimal place and another sig digit are significant – Count all numbers EXCEPT: Leading zeros Trailing zeros without a decimal point -- 2,

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, C. Significant Figures Counting Sig Fig Examples , sig figs 3 sig figs 2 sig figs

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C. Significant Figures Calculating with Sig Figs – Multiply/Divide - The # with the fewest sig figs determines the # of sig figs in the answer (13.91g/cm 3 )(23.3cm 3 ) = g 324 g 4 SF3 SF

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C. Significant Figures Calculating with Sig Figs (cont) – Add/Subtract - The # with the lowest decimal value determines the place of the last sig fig in the answer 3.75 mL mL 7.85 mL 7.9 mL 3.75 mL mL 7.85 mL

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C. Significant Figures Calculating with Sig Figs (cont) – Exact Numbers do not limit the # of sig figs in the answer Counting numbers: 12 students Exact conversions: 1 m = 100 cm 1 in any conversion: 1 in = 2.54 cm

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C. Significant Figures 5. (15.30 g) ÷ (6.4 mL) Practice Problems = g/mL 18.1 g g g g 4 SF2 SF 2.4 g/mL 2 SF

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D. Scientific Notation A way to express any number as a number between 1 and 10 (coefficient) multiplied by 10 raised to a power (exponent) Number of carbon atoms in the Hope diamond 460,000,000,000,000,000,000,000 atoms 4.6 x atoms coefficient exponent

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D. Scientific Notation Converting into Sci. Notation: – Move decimal until theres 1 digit to its left. Places moved = exponent – Large # (>1) positive exponent Small # (<1) negative exponent – Only include sig figs – all of them! 65,000 kg 6.5 × 10 4 kg

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D. Scientific Notation 7. 2,400,000 g kg km mm Practice Problems g kg km 62,000 mm

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D. Scientific Notation Calculating with Sci. Notation (5.44 × 10 7 g) ÷ (8.1 × 10 4 mol) = 5.44 EXP EE ÷ ÷ EXP EE ENTER EXE = = 670 g/mol= 6.7 × 10 2 g/mol Type on your calculator:

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D. Scientific Notation 11. (4 x 10 2 cm) x (1 x 10 8 cm) 12. (2.1 x kg) x (3.3 x 10 2 kg) 13. (6.25 x 10 2 ) ÷ (5.5 x 10 8 ) 14. (8.15 x 10 4 ) ÷ (4.39 x 10 1 ) 15. (6.02 x ) ÷ (1.201 x 10 1 ) Practice Problems cm kg x x x 10 22

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CH. 3 - MEASUREMENT Temperature Conversions

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A. Temperature Temperature – measure of the average KE of the particles in a sample of matter

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Temperature Convert these temperatures: 1)25 o C = ______________K 2)-15 o F = ______________ K 3)315K = ______________ o C 4)288K = ______________ o F

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Measurement Dimensional Analysis

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A. Problem-Solving Steps 1. Analyze 2. Plan 3. Compute 4. Evaluate

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B. Dimensional Analysis Dimensional Analysis – A tool often used in science for converting units within a measurement system Conversion Factor – A numerical factor by which a quantity expressed in one system of units may be converted to another system

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B. Dimensional Analysis The Factor-Label Method – Units, or labels are canceled, or factored out

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B. Dimensional Analysis Steps to solving problems: 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.

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C. Conversion Factors F ractions in which the numerator and denominator are EQUAL quantities expressed in different units Example: 1 in. = 2.54 cm Factors: 1 in. and 2.54 cm 2.54 cm 1 in.

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How many minutes are in 2.5 hours? Conversion factor cancel 2.5 hr 1 x xx x 60 min 1 hr = 150 min

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C. Conversion Factors Write conversion factors that relate each of the following pairs of units: 1. Liters and mL 2. Hours and minutes 3. Meters and kilometers 1 L 1000 mL 1 hr 60 min 1000 m 1 km 1000 mL 1 L =

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D. SI Prefix Conversions 1.Memorize the following chart. (next slide) 2.Find the conversion factor(s). 3.Insert the conversion factor(s) to get to the correct units. 4.When converting to or from a base unit, there will only be one step. To convert to or from any other units, there will be two steps.

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A. SI Prefix Conversions mega-M10 6 deci-d10 -1 centi-c10 -2 milli-m10 -3 PrefixSymbolFactor micro nano-n10 -9 kilo-k10 3 BASE UNIT giga-G10 9 deka-da10 1 hecto-h10 2 tera-T10 12 move left move right

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= A. SI Prefix Conversions NUMBER UNIT NUMBER UNIT 532 m = _______ km 0.532

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D. SI Prefix Conversions 1 T(base) = (base) = (base) 1 G(base) = (base) = 10 9 (base) 1 M(base) = (base) = 10 6 (base) 1 k(base) = (base) = 10 3 (base) 1 h(base) = 100 (base) = 10 2 (base) 1 da(base) = 10 (base) 1 (base) = 1 (base) 10 d(base) = 1 (base) 100 c(base) = 1 (base) 1000 m (base) = 1 (base) 10 6 µ(base) = µ(base) = 1(base) 10 9 n(base) = n(base) = 1(base) micro

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D. SI Prefix Conversions a. cm to m b. m to µm c. ns to s d. kg to g 1 m 100 cm 1 m 10 6 µm 1 s 10 9 ns 1 kg 1000 g

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D. SI Prefix Conversions 1)20 cm = ______________ m 2) L = ______________ mL 3) 45 m = ______________ m

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D. SI Prefix Conversions 4) 805 Tb = ______________ b 805 Tb b 1 Tb Terabytes bytes = 805 x bytes = 8.05 x bytes 8.05 x 10 14

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D. SI Prefix Conversions 5) 400. g = ______________ kg 6) 57 Mm = ______________ nm

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E. Dimensional Analysis Practice 1.You have $7.25 in your pocket in quarters. How many quarters do you have?

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E. Dimensional Analysis Practice 2. How many seconds are in 1.4 days? Plan: days hr min seconds

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E. Dimensional Analysis Practice 3. How many milliliters are in 1.00 quart of milk?

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E. Dimensional Analysis Practice 4.You have 1.5 pounds of gold. Find its volume in cm 3 if the density of gold is 19.3 g/cm 3.

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5. Your European hairdresser wants to cut your hair 8.0 cm shorter. How many inches will he be cutting off? E. Dimensional Analysis Practice

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6. Milton football needs 550 cm for a 1 st down. How many yards is this? E. Dimensional Analysis Practice

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7. A piece of wire is 1.3 m long. How many 1.5- cm pieces can be cut from this wire? E. Dimensional Analysis Practice

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8. How many liters of water would fill a container that measures 75.0 in 3 ?

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