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Measurement

Measurement. Scientific Notation. Rules for Working with Significant Figures:

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Measurement

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  1. Measurement

  2. Scientific Notation • Rules for Working with Significant Figures: 1. Leading zeros are never significant. 2. Imbedded zeros are always significant. 3. Trailing zeros are significant only if the decimal point is specified. Hint: Change the number to scientific notation. It is easier to see.

  3. Scientific Notation • Addition or Subtraction:The last digit retained is set by the first doubtful digit. • Multiplication or Division:The answer contains no more significant figures than the least accurately known number.

  4. Examples

  5. Examples

  6. Examples

  7. Rounding • When rounding off numbers to a certain number of significant figures, do so to the nearest value. • example: Round to 3 significant figures: 2.3467 x 104 (Answer: 2.35 x 104) • example: Round to 2 significant figures: 1.612 x 103 (Answer: 1.6 x 103) • What happens if there is a 5? There is an arbitrary rule: • If the number before the 5 is odd, round up. • If the number before the 5 is even, let it be. The justification for this is that in the course of a series of many calculations, any rounding errors will be averaged out. • example: Round to 2 significant figures: 2.35 x 102 (Answer: 2.4 x 102) • example: Round to 2 significant figures: 2.45 x 102 (Answer: 2.4 x 102) • Of course, if we round to 2 significant figures: 2.451 x 102, the answer is definitely 2.5 x 102 since 2.451 x 102 is closer to 2.5 x 102 than 2.4 x 102.

  8. Measurement • A rule of thumb: read the volume to 1/10 or 0.1 of the smallest division. (This rule applies to any measurement.) This means that the error in reading (called the reading error) is 1/10 or 0.1 of the smallest division on the glassware. • The volume in this beaker is 47 1 mL. You might have read 46 mL; your friend might read the volume as 48 mL. All the answers are correct within the reading error of 1 mL.

  9. Accuracy v. Precision Accuracy refers to how closely a measured value agrees with the correct value.Precision refers to how closely individual measurements agree with each other.

  10. Metric System

  11. Metric System

  12. Metric System

  13. Metric System

  14. Dimensional Analysis • Dimensional Analysis is a problem-solving method that uses the fact that any number or expression can be multiplied by one without changing its value.

  15. Dimensional Analysis • How many centimeters are in 6.00 inches? • Express 24.0 cm in inches.

  16. Dimensional Analysis • How many seconds are in 2.0 years?

  17. Mass v. Weight • 1) Mass is a measurement of the amount of matter something contains, while Weight is the measurement of the pull of gravity on an object. • 2) Mass is measured by using a balance comparing a known amount of matter to an unknown amount of matter. Weight is measured on a scale. • 3) The Mass of an object doesn't change when an object's location changes. Weight, on the other hand does change with location.

  18. Volume • The amount of space occupied by an object • 1 L = 1000 mL = 1000 cm 3 • 1 L = 1 cm 3 • 1 L = 1.0.57 qt • 946.1 ml = 1 qt

  19. Temperature • Measure of intensity of thermal energy • What does this mean? How hot a system is…

  20. Conversion Formulas

  21. Density • Physical characteristic • Used to id a substance • d =m/v

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