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Measurement Issues

11.1 Uncertainty and Error in Measurement. Measurement Issues. Errors Precision & Accuracy Significant Figures Scientific Notation Uncertainty. 1. Error. The error in a measurement refers to the degree of fluctuation in a measurement. Types of Experimental Error

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Measurement Issues

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  1. 11.1 Uncertainty and Error in Measurement Measurement Issues • Errors • Precision & Accuracy • Significant Figures • Scientific Notation • Uncertainty 1

  2. Error • The error in a measurement refers to the degree of fluctuation in a measurement. • Types of Experimental Error • Systematic (identifiable and can, in principle, be eliminated) • Random (positive & negative fluctuations ½ measurements too high, other ½ too low. Not always identifiable. Quantified by statistical analysis (more than 1 trial)). 2

  3. Error (cont.) • Systematic (identifiable and can, in principle, be eliminated) • Instrumental (thermometer that’s off by 2 oC) • Observational (reading of a burette) • Environmental (heating something near an AC vent) • Theoretical (simplification. Not accounting for all variables) • Random (positive & negative fluctuations ½ measurements too high, other ½ too low. Not always identifiable. Quantified by statistical analysis (more than 1 trial)). • Observational (errors in judgment of observer while reading measurement) (“human” error) • Environmental (fluctuations in voltage, temperature or mechanical vibrations) 3

  4. Error (cont.) Percent Error (% Error) Measured – Accepted x 100 = % error Accepted e.g. 9 – 10 x 100 = 10% error 10 (Absolute value) 4

  5. 11.1 Uncertainty and Error in Measurement Measurements in the laboratory will normally be made using the metric system and SI units where feasible. SI Units:NONE are DERIVATIZED (nothing calculated) length: meter (m) mass: kilogram (kg) *note: only base unit that uses a prefix time: second (s) electric current: ampere (A) thermodynamic temperature:kelvin (K) amount of substance: mole (mol) luminous intensity: candela (cd) 5

  6. 11.1.2 Accuracy and Precision • Accuracy is the degree of closeness of a measured or calculated quantity to its actual (true) value. • Precision is also called reproducibility or repeatability. It is the degree to which further measurements or calculations show the same or similar results. In other words • Accuracy refers to the proximity of a measurement to the true value of a quantity. • Precision refers to the proximity of several measurements to each other. 6

  7. 11.1 Uncertainty and Error in Measurement Accuracy and Precision A measurement may be either accurate or precise, both or neither. 7

  8. 11.1 Uncertainty and Error in Measurement Significant Figures A measurement is always limited by the precision of the Instrument. An understanding of significant figures is important to express the appropriate precision of a measurement. • Only zeros are non-significant digits (but not all always) • There are cases where a zero may be significant: - A Zero between 2 non-zeros digits. (e.g. 103 cm, yes) - Numbers less than 1, Zeros in front of the first non zero digit are not significant. (after start counting, they are significant) e.g. 0.002030 km (the last zero indicates measurement has been made that far out). - Numbers greater than 1, Zeros at the end of numbers do not refer to a precise count 980000 (Exception: a decimal point orbar over zero; 300. or 300) 8

  9. Significant Figures • 0.004070 -- The zeros shown in red are not significant. The number is precise to 4 significant digits • With numbers having a zero at the end the number of significant figures depends on the precision with which the number is known (how far was it measured). • 40000-- one significant digit. The number is known to the nearest ten thousand. • 40000-- three significant digits. The number is known to the nearest hundred. • 40000-- five significant digits. The number is known to the nearest unit. _ _ 9

  10. Significant Figures Answers: 3 1 5 1 4 8 4 5 Practice: # of sig figs • 101 • 200 • 100.00 • 0.0008 • 0.005600 • 30 780 000 • 30 780 000 • 30 780 000 _ _ 10

  11. Scientific Notation • Large numbers are hard to visualize. Scientific notation writes numbers in two parts: • a number between 1 and less than 10 and • a power of 10 • Examples • 30 000 000 is represented as 3 x 107 • 30 000 000. is represented as 3.0000000 x 107 • 0.0000482 is represented as 4.82 x 10-5 • Note: The numbers present in Sci. Not. are SIGNIFICANT!!! 11

  12. Scientific Notation • Answers: • 6.5 x 10-3 • 2.15 x 104 • 1.408 x 10-1 • 5.8942 x 105 • 1 x 10-10 • 2 x 1016 Practice: • 0.0065 • 21 500 • 0.1408 • 589420 • 0.000 000 000 1 • 20 000 000 000 000 000 12

  13. Significant Figures • Math Functions: Addition/subtraction: • When adding or subtracting, answer will have FEWEST decimal places. • Dumb People Are Stupid Multiplying/dividing: • When multiplying or dividing, answer with fewest Sig. Figs. • My Dad Sells Fireworks 13

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