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Understanding Measurements: Accuracy, Precision, and Their Importance in Science

Measurements are fundamental in providing a clear description of nature by quantifying attributes such as length, time, and speed. They form the backbone of scientific theories, laws, and principles, lending credibility to interpretations when coupled with accuracy and precision. This guide explores the definition of measurements, the role of significant figures, concepts of uncertainty, and calculations in scientific notation. Understanding these elements is essential for achieving reliable and meaningful results in any scientific endeavor.

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Understanding Measurements: Accuracy, Precision, and Their Importance in Science

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  1. Measurements

  2. Measurements A very concrete method of dealing with the description, size and understanding of nature

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

  4. Measurements A very concrete method of dealing with the description, size, 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. Measurements • What is a measurement?

  6. Measurements What is a measurement? • It is a quantity.

  7. Measurements What is a measurement? • It is a quantity. • It almost always requires both a magnitude (number) and a unit.

  8. Measurements What is a measurement? • It is a quantity. • It almost always requires both a magnitude (number) and a unit. • Unit can be: • Length • Time • Speed or velocity • Any thing that gives a description of the magnitude

  9. What is a measurement? • It is a quantity. • It almost always requires both a magnitude (number) and a unit. Examples: 3 meter 3m 15 seconds 15s 12 meters/second 12m/s

  10. With out both the magnitude and unit the measurement would have no meaning

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

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

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

  14. All measuring devices have a certain amount of uncertainty

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

  16. 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) • The skill of the person performing the measurement is also a factor in precision • Accuracy is how close the measurement is to the true value • Influenced by : • person making the measurements • precision of the instrument

  17. 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:

  18. MAGNIFY

  19. MAGNIFY The right edge of the ruler is at 8.8 + ? The Left edge of the ruler is set where? exactly at zero left or right of zero

  20. 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

  21. 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

  22. 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

  23. 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.

  24. 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 by using the correct 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

  25. 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

  26. 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

  27. 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 order of magnitude Volume ≈106m3

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