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