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MEASUREMENT (A Quantitative Observation)

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 .

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MEASUREMENT (A Quantitative Observation)

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  1. 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.

  2. 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.

  3. 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

  4. 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

  5. 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%

  6. A way to express very large or very small numbers easily. Example: .0000000000000036333 seconds = 3.6333 x 10-15 seconds SCIENTIFIC NOTATION 9876500000000 minutes = 9.8765 x 1012 minutes

  7. Practice (1) .000565 g • 5.65 x 10-4 g (2) 565000 s • 5.65 x 105 s (3) 43454 min • 4.3454 x 104 min (4) .0010 L • 1.0 x 10-3 L

  8. 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.

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

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

  11. 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.

  12. 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.

  13. 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)

  14. Putting It ALL Together

  15. the speed of light = 299 792 458 m / s 9 significant figures (sig figs) 2.99 792 458 x 108 m/s 8 sig figs = 2.99 792 46 x 108 m/s 7 sig figs = 2.99 792 5 x 108 m/s 6 sig figs = 2.99 792 x 108 m/s 5 sig figs = 2.99 79 x 108 m/s 4 sig figs = 2.99 8 x 108 m/s 3 sig figs = 3.00 x 108 m/s 2 sig figs = 3.0 x 108 m/s 1 sig figs = 3 x 108 m/s

  16. ROUNDING 123 456 789 • 123456790 • 123456800 • 123457000 • 123460000 • 123500000 • 123000000 • 120000000 • 100000000 = 1.2345679 x 108 = 1.234568 x 108 = 1.23457 x 108 = 1.2346 x 108 = 1.235 x 108 = 1.23 x 108 = 1.2 x 108 = 1 x 108

  17. 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

  18. 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

  19. Answers in Scientific Notation • 1.0x 100 blah 2 sig figs • 1.000000000x 108 blah 10 sig figs • 1 x 102 blah 1 sig fig • 1.00x 102 blah 3 sig figs • 1.0 x 10-1 blah 2 sig figs • 1x 10-2 blah 1 sig fig • 1.0x 10-2 blah 2 sig figs • 1.01 x 102 blah 3 sig figs

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