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I II III I. Units of Measurement Chapter 2 – Scientific Measurement

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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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Same object with different rulers: C. Significant Figures

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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 -- 0.0025 Trailing zeros without a decimal point -- 2,500 5085 2.60 739

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4. 0.080 3. 5,280 2. 402 1. 23.50 C. Significant Figures Counting Sig Fig Examples 1. 23.50 2. 402 3. 5,280 4. 0.080 4 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 ) = 324.103g 324 g 4 SF3 SF

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C. Significant Figures Calculating with Sig Figs (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 224 g + 130 g 354 g 7.9 mL 350 g 3.75 mL + 4.1 mL 7.85 mL 224 g + 130 g 354 g

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C. Significant Figures Calculating with Sig Figs (cont’d) 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 = 2.390625 g/mL 18.1 g 6. 18.9g - 0.84 g 18.06 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 4.6 x 10 23 Mass of one carbon atom 0.00000000000000000000002 g 2 x 10 -23 g coefficient exponent

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D. Scientific Notation Converting into Sci. Notation: Move decimal until there’s 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 8. 0.00256 kg 9. 7.0 10 -5 km 10.6.2 10 4 mm Practice Problems 2.4 10 6 g 2.56 10 -3 kg 0.000070 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 78.1 4 = 671.6049383= 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 10 -4 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 10 23 ) ÷ (1.201 x 10 1 ) Practice Problems 4 10 10 cm 2 6.9 10 -2 kg 2 1.1 x 10 -6 1.86 x 10 3 5.01 x 10 22

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Homework Complete Worksheet “Using Measurements – Chapter 2”: due tomorrow!

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II. Unit Conversions CH. 2 – MEASUREMENT

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A. SI Prefix Conversions 1.Find the difference between the exponents of the two prefixes. 2.Move the decimal that many places. To the left or right?

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

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A. SI Prefix Conversions mega-M10 6 deci-d10 -1 centi-c10 -2 milli-m10 -3 PrefixSymbolFactor micro- 10 -6 nano-n10 -9 pico-p10 -12 kilo-k10 3 move left move right BASE UNIT---10 0

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A. SI Prefix Conversions 1) 20 cm = ______________ m 2) 0.032 L = ______________ mL 3) 45 m = ______________ nm 4) 805 dm = ______________ km 0.2 0.0805 45,000 32

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B. Derived Units Combination of base units. Volume (m 3 or cm 3 ) length length length D = MVMV 1 cm 3 = 1 mL 1 dm 3 = 1 L Density (kg/m 3 or g/cm 3 ) mass per volume

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C. Density Mass (g) Volume (cm 3 )

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C. Density An object has a volume of 825 cm 3 and a density of 13.6 g/cm 3. Find its mass. GIVEN: V = 825 cm 3 D = 13.6 g/cm 3 M = ? WORK : M = DV M = (13.6 g/cm 3 )(825cm 3 ) M = 11,200 g

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C. Density A liquid has a density of 0.87 g/mL. What volume is occupied by 25 g of the liquid? GIVEN: D = 0.87 g/mL V = ? M = 25 g WORK : V = M D V = 25 g 0.87 g/mL V = 29 mL

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I II III III. Dimensional Analysis Conversion Factors Problems CH. 2 – MEASUREMENT

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A. Vocabulary 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: 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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Fractions 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. C. Conversion Factors

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

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Conversion factor cancel By using dimensional analysis / factor-label method, the UNITS ensure that you have the conversion right side up, and the UNITS are calculated as well as the numbers! How many minutes are in 2.5 hours? 2.5 hr 1 x xx x 60 min 1 hr = 150 min

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You have $7.25 in your pocket in quarters. How many quarters do you have? X = 29 quarters D. Dimensional Analysis Practice 7.25 dollars 1 dollar 4 quarters

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How many seconds are in 1.4 days? Plan: days hr min seconds 1.4 days x 24 hr x 60 min x 60 sec = 1 1 day1 hr 1 min E. Dimensional Analysis Practice 120960 sec 120000 sec 1.2 x10 5 sec

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D. Dimensional Analysis Practice How many milliliters are in 1.00 quart of milk? 1.00 qt 1 L 1.057 qt = 946 mL qtmL 1000 mL 1 L

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You have 1.5 pounds of gold. Find its volume in cm 3 if the density of gold is 19.3 g/cm 3. lbcm 3 1.5 lb 1 kg 2.2 lb = 35 cm 3 1000 g 1 kg 1 cm 3 19.3 g D. Dimensional Analysis Practice

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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? 8.0 cm1 in 2.54 cm = 3.1 in cmin D. Dimensional Analysis Practice

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6) Roswell football needs 550 cm for a 1st down. How many yards is this? 550 cm 1 in 2.54 cm = 6.0 yd cmyd 1 ft 12 in 1 yd 3 ft D. 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? 1.3 m 100 cm 1 m = 86 pieces mpieces 1 piece 1.5 cm D. Dimensional Analysis Practice

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How many liters of water would fill a container that measures 75.0 in 3 ? 75.0 in 3 (2.54 cm) 3 (1 in) 3 = 1.23 L in 3 L 1 L 1000 cm 3 D. Dimensional Analysis Practice

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