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MEASUREMENT (A Quantitative Observation) MEASUREMENTS always have 2 things: Number & Unit All measurements have error in them! A measurement consists of all known digits that can be known accurately PLUS one digit that is ESTIMATED. The estimated digit is always at the END of the number in a measurement.

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MEASUREMENT & Degrees of Error The closer a measurement is to the true value, the more accurate the measurement. Accurate measurements are “more correct” and closer to the true value. Accuracy = Correctness. How close a series of measurements are to one another is called precision. Precise measurements are close in value to one another; repeated measures are precise. Precision = Reproducibility.

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Accuracy vs. Precision Another example: a 5 lb bag of potatoes is weighed by 3 people, 3 times each. Person 1 4.9 lbs 4.8 lbs 4.85 lbs Person 2 4.0 lbs 3.5 lbs 5 lbs Person 3 4.0 lbs 4.1 lbs 4.2 lbs Good Accuracy Good Precision Poor Accuracy Poor Precision Poor Accuracy Good Precision

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Determining Error Accepted value is the correct value based on reliable references. Reference: boiling point of water is 100.0°C Experimental value: temperature of boiling water measured to be 99.1°C ERROR = experimental – accepted value

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ERROR = (99.1°C – 100.0 °C) = –0.9 °C (-) means your measurement was less than the number of the true value. (+) means your measurement is greater than the true value. PERCENT ERROR is an absolute value: %ERROR = (0.9/100) x 100 = 0.9%

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A way to express very large or very small numbers easily. Example:.0000000000000036333 seconds = 3.6333 x 10 -15 seconds = 9.8765 x 10 12 minutes 9876500000000 minutes SCIENTIFIC NOTATION

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Practice (1).000565 g 5.65 x 10 -4 g (2) 565000 s 5.65 x 10 5 s (3) 43454 min 4.3454 x 10 4 min (4).0010 L 1.0 x 10 -3 L

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Measurement Limitations ALL measurements have error in them! A measurement consists of all known digits that can be known accurately PLUS one digit that is estimated. The estimated digit is always at the end of the number in a measurement. All of the digits that are known in a measurement are significant figures. Fewer significant figures = more rounding in a measurement = more error.

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What are the following lengths (in meters)? (A) (B) (C)

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ANSWERS (A) 0.3 m (1 decimal place) (B) 0.26 m (2 decimal places) (C) 0.260 m (3 decimal places)

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What is the density of a sample with a mass of 24.47 g and a volume of 13.2 mL? A. 1.9 g/mL B. 1.8537 g/mL C. 1.854 g/mL D. 1.85 g/mL APPLYING SIG FIGS to MEASUREMENT: HINT: Your FINAL answer cannot be more accurate than the least accurate measurement.

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What is the density of a sample with a mass of 24.47 g and a volume of 13.2 mL? A. 1.9 g/mL B. 1.8537 g/mL C. 1.854 g/mL D. 1.85 g/mL APPLYING SIG FIGS to MEASUREMENT: Because 13.2 mL is accurate to only one decimal place, the answer can be no more accurate than one decimal place.

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Easy Rules To Sig Figs ALL trailing zeros in a non-decimal are NOT significant (they act as placeholders only) ALL leading zeros in a decimal are NOT significant (they act as placeholders only) Sandwhiched zeros count (i.e. 101, 0.101) In a decimal, if the zero in question has a number 1 thru 9 before it anywhere in the number, it is significant! (i.e. 0.000000100000)

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Putting It ALL Together

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the speed of light = 299 792 458 m / s 9 significant figures (sig figs) 2.99 792 458 x 10 8 m/s 8 sig figs = 2.99 792 46 x 10 8 m/s 7 sig figs = 2.99 792 5 x 10 8 m/s 6 sig figs = 2.99 792 x 10 8 m/s 5 sig figs = 2.99 79 x 10 8 m/s 4 sig figs = 2.99 8 x 10 8 m/s 3 sig figs = 3.00 x 10 8 m/s 2 sig figs = 3.0 x 10 8 m/s 1 sig figs = 3 x 10 8 m/s

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ROUNDING 123 456 789 123456790 123456800 123457000 123460000 123500000 123000000 120000000 100000000 = 1.2345679 x 10 8 = 1.234568 x 10 8 = 1.23457 x 10 8 = 1.2346 x 10 8 = 1.235 x 10 8 = 1.23 x 10 8 = 1.2 x 10 8 = 1 x 10 8

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Determine the Significant Figures 1.0 blah 100000000.0 blah 100 blah 100. blah 0.10 blah 0.01 blah 0.010 blah 101 blah

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Answers 1.0 blah 2 sig figs 100000000.0 blah 10 sig figs 100 blah 1 sig fig 100. blah 3 sig figs 0.10 blah 2 sig figs 0.01 blah 1 sig fig 0.010 blah 2 sig figs 101 blah 3 sig figs

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Answers in Scientific Notation 1.0 x 10 0 blah 2 sig figs 1.000000000 x 10 8 blah 10 sig figs 1 x 10 2 blah 1 sig fig 1.00 x 10 2 blah 3 sig figs 1.0 x 10 -1 blah 2 sig figs 1 x 10 -2 blah 1 sig fig 1.0 x 10 -2 blah 2 sig figs 1.01 x 10 2 blah 3 sig figs

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