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Measurements

Measurements . Measurements . A very concrete methods of dealing with the description and understanding of nature. Measurements . A very concrete method of dealing with the description and understanding of nature Measurements give credibility to the interpretation of; Theories Laws

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Measurements

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  1. Measurements

  2. Measurements A very concrete methods of dealing with the description and understanding of nature

  3. Measurements A very concrete method of dealing with the description and understanding of nature Measurements give credibility to the interpretation of; Theories Laws Principles Hypothesis

  4. Measurements A very concrete way of dealing with the description and understanding of nature Measurements give credibility to the interpretation of: Theories Laws Principles Hypothesis This credibility is directly related to the accuracy of the measurements

  5. Estimation (uncertainty) • All measurements have some degree of estimation.

  6. It would be difficult to measure with an certainty beyond a millimeter

  7. The ruler has a limited amount of certainty. Thinner lines could increase the amount of certainty .

  8. All measuring devices have a certain amount of uncertainty

  9. The uncertainty of a measurement is determined by the a. precision of the measurement and b. accuracy of the measured value

  10. Precision verses Accuracy • Precision in its strictest sense refers to the exactness to which the measuring instrument has been manufactured. • If the same measurement is repeated multiple times with the same instrument, will the measurement be the same each time? (repeatability) • smaller units would make the instruments more precise (exact_ • Accuracyis how close the measurement is to the true value • Influenced by : • person making the measurements • precision of the instrument

  11. Measurement of Uncertainty • Estimated uncertaintyis written with a ± sign; for example: • Percent uncertaintyis the ratio of the uncertainty to the measured value, multiplied by 100:

  12. Significant Figures • The number of significant figuresis the number of reliably known digits in a number. It is usually possible to tell the number of significant figures by the way the number is written: • 23.21 cm has 4significant figures • 0.062 cm has 2 significant figures (the initial zeroes don’t count) • 80 km is ambiguous – it could have 1or2significant figures. If it has 3,it should be written 80.0 km. If it has 2 it should be written in scientific notation 8.0 x 101km

  13. Significant Figures • Whenmultiplyingordividingnumbers, the result has as many significant figures as the number used in the calculation with the fewest significant figures. • Example: 11.3 cm x 6.8 cm = 76.84 cm2 77 cm2 • 11.3 cm / 77cm = 0.1467 0.15

  14. Adding and Subtracting Significant Figures • When adding or subtracting quantities, leave the same number of decimal places (rounded) in the answer as there are in the quantity with the least number of decimal places. • Examples 1) 2) 23.1 157 0.546 -5.5 1.45 151.5 152 25.096 25.1

  15. 1-4 Measurement and Uncertainty; Significant Figures Calculators will not give you the right number of significant figures; they usually give too many but sometimes give too few (especially if there are trailing zeroes after a decimal point). The top calculator shows the result of 2.0 / 3.0. The bottom calculator shows the result of 2.5 x 3.2.

  16. Scientific Notation • Scientific notation is the expression of a number in the “power of 10” • 36,900 3.69 x 104 • allows a number to expressed in significant digits in the coefficient • eliminates the need to write multiple zeros Know how to add, subtract, multiply, and divide numbers expressed in scientific notation

  17. Order of Magnitude Estimation • Method of making an approximate value for a measurement • the number is rounded to one (1) significant figure • and its power of 10 3,675 m ----- 4 x 103 m 5,000 m ----- 5 x 103 m added together 9 x 103 m

  18. Order of Magnitude Estimation • Reasons for • Rapid estimation • Accurate calculation is not worth the time • Quick check of an accurate calculation to check for large errors • Check the accuracy of the exponent

  19. Order of Magnitude Example • Find the volume (V) of a lake • Lake has • Average depth of 65 m • Surface area of 52,500 m2 Volume = area x depth = (7 x 101m) x (5 x 104m2) = 3.5 x 106m3

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