Error in Measurement

1. Error in Measurement • Some error or uncertainty always exists in any measurement. • skill of the measurer • limitations of measuring instruments • When recording measurements, report all digits known for certain plus one last digit that is an estimate.

2. Recording Measurements • Record the volume of liquid in the graduated cylinder to the correct number of digits.

3. RULES FOR DETERMINING SIGNIFICANT FIGURES • Rule #1: Nonzero digits always count as significant figures: Examples: 438 g _____ sig fig 26.42 m _____ sig fig 1.7 cm _____ sig fig 0.653 L _____ sig fig

4. Rule #2: Captive zeros always count as significant figures: Examples: 506 dm _____ sig fig 1005 mL _____ sig fig 900.43 kg _____ sig fig 20.006 cm _____ sig fig • Rule #3: Leading zeros do not count as significant figures: Examples: 0.8 g _____ sig fig 0.06 g _____ sig fig 0.0047 L _____ sig fig

5. Rule #4: Trailing zeros are significant only if the number contains a decimal point: Examples: 60 g _____ sig fig 4830 km _____ sig fig 8.0 dm _____ sig fig 1.60 sec _____ sig fig 35.000 L _____ sig fig 0.002450 kg _____ sig fig

6. RULES FOR ROUNDING OFF NUMBERS • If the digit immediately to the right of the last significant figure you want to retain is: • Less than 5------ the last significant digit should stay the same. Example: Round 17.32 m to 3 significant figures. • Since the 2 is less than 5, you should round to __________ m

7. 5 or greater --------- the last significant figure should increase by 1. Example: Round 42.68 g to 3 significant figures. • Since 8 is greater than 5, you should round to __________ g

8. What Do You Think? • Determine the number of significant figures in each of the following: a. 12.045 d. 12.0 b. 0.0028 e. 0.500 c. 6500 f. 16.002070 • Round each of the following to 2 significant figures. • 5.2836 b. 0.06382 c. 3196 • Explain how the measurement 6.2 cm is different from 6.20 cm.