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3.1 Measurement and Uncertainty

3.1 Measurement and Uncertainty. How do you think scientists ensure measurements are accurate and precise?. Expressing Measurements. Scientific Notation Coefficient and power of 10 Example – 6.02 x 10 23 Useful in expressing very large and very small numbers

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3.1 Measurement and Uncertainty

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  1. 3.1 Measurement and Uncertainty How do you think scientists ensure measurements are accurate and precise?

  2. Expressing Measurements • Scientific Notation • Coefficient and power of 10 • Example – 6.02 x 1023 • Useful in expressing very large and very small numbers • What power of 10 would a very small number like 0.00000015 be? • 1.5 x 10-7

  3. Is the Measurement Right? • Accuracy – How close a measurement is to the actual or true value. Need actual or true value to compare • Precision – How close a series of measurements are to one another. Need to have 2 or more repeated measurements (Dart Board Situation)

  4. Determining Error • Accepted Value – Correct value based on reliable reference • Experimental Value – Measurement from the investigation • Error - The difference between the experimental and accepted values. Error = Experimental value – Accepted value

  5. Percent Error • The absolute value of the error divided by the accepted value, then multiplied by 100%. Percent Error = [error]/accepted value x 100% Why the absolute value of the error?

  6. Practice • Measure the mass of your toy car using the triple beam balance. • Use the electronic scale to determine the true mass value for the toy car. • Calculate the percent error for your measurement. • How many significant figures does your mass measurement have?

  7. Significant Figures • All the digits that are know plus the last digit that is estimated. (Used for the purpose of rounding.) • Rules for Sig. Figs. • All nonzero digits are significant. • Zeros appearing between nonzero digits are significant. • Leftmost zeros appearing in from of nonzero are not significant (just placeholders). Try sci not. • Zeros at the end and to the right of a decimal point are always significant. • Zeros at the rightmost end that lie to the left of the decimal point are not significant. Try sci not. • Exact quantities do not affect the process of rounding

  8. How many significant figures? • 0.05730 meters • 8765 kilograms • 0.00073 centimeters • 20 flags • 40.007 liters • 8.750 x 10-2 grams Then round to 2 significant figures.

  9. Significant Figures for Calculations • Answer cannot be more precise than the least precise measurement in which it was calculated from. Addition and Subtraction 2.34 + 45.1 + 8.706 = 56.146 Rounded to 56.1 (to the tenth) Multiplication and Division 8.09 x 7.861 x 3.112 = 197.9091649 Rounded to 198 (to 3 significant figures)

  10. Do the math and put the answer in the correct number of significant figures. • 75.9 m + 8.72 m + 9.8 m • 5.66 L – 3.221 L • 4.90 grams + 17.987 grams • 3.75 cm – 1.2 cm • 12.4 grams + 8.65 grams + 9.214 grams • 14.2 kilograms – 7.146 kilograms

  11. Do the same with multiplication and division. • 7.09 meters x 6.2 meters • 23.5 cm x 8.2 cm x 14.9 cm • 5467 ml / 14.6 • 7875.9 meters x (1 km/1000 meters) • 3.9823 liters / 43.1 liters • 678 seconds / 8 Now put your answer in scientific notation.

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