1 / 26

MEASUREMENT & SIGNIFICANT FIGURES

11.65 cm. Are you sure?. MEASUREMENT & SIGNIFICANT FIGURES. MEASUREMENT ERRORS. SYSTEMATIC ERRORS. Are are reproducible inaccuracies that are consistently in the same direction. Systematic errors are often due to a problem which persists throughout the entire experiment.

efia
Download Presentation

MEASUREMENT & SIGNIFICANT FIGURES

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 11.65 cm Are you sure? MEASUREMENT & SIGNIFICANT FIGURES

  2. MEASUREMENT ERRORS

  3. SYSTEMATIC ERRORS • Are are reproducible inaccuracies that are consistently in the same direction. • Systematic errors are often due to a problem which persists throughout the entire experiment. • Eliminating Systematic Errors can increase accuracy. • Associated with particular measurement instruments or techniques. • Data apt to be too high or too low. • Sometimes referred to as bias. • Examples • Experimental conditions • Air resistance • Friction • Environmental conditions (temp, humidity, pressure) • Instrument limitations • Shoddy construction • Faulty calibration • Metal parts (affect of heat) • Personal (human) error • Parallax – shift of position • Reflex • Reading instrument

  4. PARALLAX – Shift of Position • This error can occur whenever there is some distance between the measuring scale and the indicator used to obtain a measurement. If the observer's eye is not squarely aligned with the pointer and scale, the reading may be too high or low

  5. RANDOM ERRORS • Are statistical fluctuations (in either direction) in the measured data due to the precision limitations of the measurement device. • Random errors usually result from the experimenter's inability to take the same measurement in exactly the same way to get exact the same number. • Eliminating Random errors increases precision. • Error often lies with imperfect observation or technique. • Examples • Environmental conditions • Fluctuations in conditions (Temperature, humidity, pressure) • Instrumental limitations • Mechanical vibrations • Limitations of instrument (number of significant figures) • Personal (human) error • Misjudging the estimated reading on an instrument • Must work to person’s limit

  6. RANDOM & SYSTEMATIC ERRORS

  7. MEASUREMENT ERRORS • ACCURACY-denotes how close you are to the accepted value • Expressed in terms of • Absolute error - difference between observed value and accepted value. Experimental error • Percent error - absolute error compared to accepted value. % error

  8. ACCURACY EXAMPLE • In an experiment to measure the acceleration due to gravity, 9.96 m/s2 is experimentally determined. • Find the absolute error and the % error, given the accepted value is 9.81 m/s2

  9. MEASUREMENT ERRORS • PRECISION-Agreement between numerical values in a set of measurements that have been made the same way. • Reproducibility of results • The SPREAD of the results • How close are they? • A large degree of precision does not necessarily imply accuracy! • Obtaining greater accuracy for an experimental value depends on minimizing systematic errors. • Obtaining greater precision for an experimental value depends on minimizing random error.

  10. Good Accuracy & Precision Good Accuracy Good Precision ACCURACY VS PRECISION

  11. Range= 0.01 g Range = 0.22 g PRECISION EXAMPLE • Two independent experiments give two sets of data for measuring the mass of a 100.00 g cylinder. • Which set, A or B has the best precision, based on its range?

  12. PRECISION EXAMPLE 2 • The readings from a thermometer taken with two different thermometers are as follows. • Thermometer A measures 98.6o F • Thermometer B measures 98.67o F • Which measurement is more precise?

  13. SIGNIFICANT FIGURES • Defined as all the digits in a measurement that you are certain of plus the first uncertain digit • Sig figs are used because all instruments have limits and we must limit the number of digits we report our results

  14. INSTRUMENT LIMITATIONS 4.3 cm 83 ml 4.32 cm 4.3 cm 11.65 cm 4.40 cm

  15. 9.00 cm HOW LONG IS THE GREEN LINE?

  16. SIGNIFICANT FIGURES SIGNIFICANT FIGURE RULES 6 Sig figs 1. All non-zero digits are significant • 235.987 km 4 Sig figs 3 sig figs 2. Any final zero(s) used AFTER the decimal point is/are significant • 24.0 seconds 0.7830 newton-meters • 987.00 grams 5 Sig figs 6 Sig figs 3. Zeros between two other sig figs are significant • 3089.09 newtons

  17. 1 2 3 4 5 FIND THE AREA OF THE RECTANGLE

  18. 1.24 cm 1 2 3 3 4 4 5 5 ‘4’ is an Uncertain Digit 2 1

  19. 5.08 cm 1 2 3 4 5 1 2 3 4 5 ‘8’ is an Uncertain Digit

  20. 1 2 3 4 5 ‘4’ is an Uncertain Digit ‘8’ is an Uncertain Digit 1.24 cm 5.08 cm ‘4’ is an Uncertain Digit Length = 5.08 cm - 1.24 cm = 3.84 cm 3 Significant Figures

  21. 1 2 3 4 5 MEASURE THE WIDTH

  22. 2 1 2 3 4 5 1 1.53 cm ‘3’ is an UncertainDigit

  23. 3.65 cm 4 1 2 3 4 5 3 ‘5’ is an Uncertain Digit

  24. 1 2 3 4 5 3.65 cm ‘2’ is an Uncertain Digit 1.52 cm Width = 3.65 cm - 1.53 cm = 2.12 cm 3 Significant Figures

  25. 3.84 cm 3.84 cm 2.12 cm 2.12 cm 768 384 768 8.1408 cm2 Surface Area Three significant figures in the product 8.14 cm2

  26. SIGNIFICANT FIGURES RESULTS • Addition or Subtraction • The result will have the same number of decimal places as the quantity with the least number of decimal places that was used in the calculation. • Multiplication or Division • The result will have the same number of significant figures as the quantity with the least number of significant figures that was used in the calculation.

More Related