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 10 23  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. 1. All nonzero digits are significant. 2. Zeros appearing between nonzero digits are significant. 3. Leftmost zeros appearing in from of nonzero are not significant (just placeholders). Try sci not. 4. Zeros at the end and to the right of a decimal point are always significant. 5. Zeros at the rightmost end that lie to the left of the decimal point are not significant. Try sci not. 6. Exact quantities do not affect the process of rounding

8. How many significant figures? 1. 0.05730 meters 2. 8765 kilograms 3. 0.00073 centimeters 4. 20 flags 5. 40.007 liters 6. 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. 1. 75.9 m + 8.72 m + 9.8 m 2. 5.66 L – 3.221 L 3. 4.90 grams + 17.987 grams 4. 3.75 cm – 1.2 cm 5. 12.4 grams + 8.65 grams + 9.214 grams 6. 14.2 kilograms – 7.146 kilograms

11. Do the same with multiplication and division. 1. 7.09 meters x 6.2 meters 2. 23.5 cm x 8.2 cm x 14.9 cm 3. 5467 ml / 14.6 4. 7875.9 meters x (1 km/1000 meters) 5. 3.9823 liters / 43.1 liters 6. 678 seconds / 8 Now put your answer in scientific notation.