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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. 65,000 kg 6.5 × 10 4 kg

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Scientific Notation 1. 2,400,000 g 2. 0.00256 kg 3.7 10 -5 km 4. 6.2 10 4 mm Practice Problems 2.4 10 6 g 2.56 10 -3 kg 0.00007 km 62,000 mm

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Calculating with Scientific Notation Example: (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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Accuracy and Precision Percent Error Significant Figures Chemistry Math

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A. Accuracy vs. Precision Accuracy – a measure of how close a measurement comes to the true value Precision – a measure of how close a series of measurements are to one another. ACCURATE = CORRECT PRECISE = CONSISTENT

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Example: Low accuracy – high precision High accuracy – low precision High accuracy – high precision

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B. Calculating Percent Error Error – the difference between the experimental value and the accepted value. your value true 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 and the % error if the accepted value of the density is 1.36 g/mL.

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SIGNIFICANT FIGURES A New Way To Count Numbers

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C. Significant Figures Indicates the precision of a measurement. Recording Sig Figs –Sig figs in a measurement include the known digits plus a final estimated digit 2.35 cm

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2.83 cm 4.50 cm 15.0 o C28.5 o C30.0 mL4.29 mL

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C. Significant Figures Counting Sig Figs –Count all numbers EXCEPT: »Leading zeros -- 0.0025 »Trailing zeros without a decimal point -- 2,500

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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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NON ZERO DIGITS A non zero digit is any number but zero 4, 6, 12, 7, 9, 1 are all non zero digits 1.48593 62.7

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CAPTIVE ZEROS Captive zeros are those in between two numbers 604 1.007 60.4057

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LEADING ZEROS Leading zeros are zeros at the beginning of the number. 0.0042 0.000008

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TRAILING ZEROS Zeros that come at the end of a number 450 1.600 30.0 ZEROS

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Scientific Notation All numbers in the first number are significant. 3.40 X 10 -5 6.02 x 10 23 9.64 x 10 -10

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C. Significant Figures Calculating with Sig Figs –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 –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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EXACT NUMBERS 1.Exact numbers have infinite number of significant figures. Exact numbers include 1.Counting of anything : 22 people or 10 meter sticks, 6 eggs etc. 2.Defined quantities : 12 = 1 doz. 2.Exact numbers do not affect the rounding to the correct number of significant figures or in the calculations of the measurements.

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C. Significant Figures 1. (15.30 g) ÷ (6.4 mL) Practice Problems = 2.390625 g/mL 18.1 g 2. 18.9g - 0.84 g 18.06 g 4 SF2 SF 2.4 g/mL 2 SF

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Practice Problems (pg. 70 &71). 3). 61.2 meters + 9.35 meters + 8.6 meters = 4). 8.3 meters x 2.22 meters= 5). 8.345 g / 10.6 mL =

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