2. Significant Figures Chemistry 10 Chemistry 10

3. Significant figures: the number of digits in an experimentally derived number that give useful information about the data quality Data with many significant figures (sig. figs.) is considered to be precise, and usually implies greater accuracy. Sig. figs. show how “good” our instruments are to anybody looking at the data Significant figures: the number of digits in an experimentally derived number that give useful information about the data quality Data with many significant figures (sig. figs.) is considered to be precise, and usually implies greater accuracy. Sig. figs. show how “good” our instruments are to anybody looking at the data

4. Accuracy: a measure of how close a measured value is to the actual value Precision: a measure of how reproducibly a measurement can be taken A paper clip’s mass is measured 3 times and the following values are obtained: 1.0025g, 1.0026g, and 1.0025g. What does this indicate? If the paper clip’s actual mass is 1.9871g, the measurements above are not ___________ because they don’t reflect the true mass. Accuracy: a measure of how close a measured value is to the actual value Precision: a measure of how reproducibly a measurement can be taken A paper clip’s mass is measured 3 times and the following values are obtained: 1.0025g, 1.0026g, and 1.0025g. What does this indicate? If the paper clip’s actual mass is 1.9871g, the measurements above are not ___________ because they don’t reflect the true mass.

5. When writing down a measurement, write all of the digits obtained directly with the measuring device and add a final, estimated digit. Example: a ruler whose smallest mark is 1 millimeter can measure lengths in 1/10 of a millimeter. When writing down a measurement, write all of the digits obtained directly with the measuring device and add a final, estimated digit. Example: a ruler whose smallest mark is 1 millimeter can measure lengths in 1/10 of a millimeter.

6. Rules for identifying and writing Sig. Figs. 1. All nonzero digits are significant 2. Zeros a. Leading zeros: zeros written to the left of all nonzero digits are not significant b. Captive zeros: zeros written between nonzero digits are significant c. Trailing zeros: zeros written to the right of all nonzero digits are only significant if a decimal point is present. 3. Scientific notation: only digits in the portion before the “  10 n ” are significant 1. All nonzero digits are significant 2. Zeros a. Leading zeros: zeros written to the left of all nonzero digits are not significant b. Captive zeros: zeros written between nonzero digits are significant c. Trailing zeros: zeros written to the right of all nonzero digits are only significant if a decimal point is present. 3. Scientific notation: only digits in the portion before the “  10 n ” are significant

7. How many significant figures? 235 0.000345 20 017.5 14 000 14 000.0 2.74  10 -7 7.20004  10 8 235 0.000345 20 017.5 14 000 14 000.0 2.74  10 -7 7.20004  10 8 3 3 6 2 6 3 6

8. Sig. Figs. in calculations 1. Addition and Subtraction Round off the calculated result to match the number with the leftmost uncertain (estimated) digit 1. Addition and Subtraction Round off the calculated result to match the number with the leftmost uncertain (estimated) digit

9. Sig. Figs. in calculations Multiplication and Division Round off the calculated result to the same number of significant figures as the measurement with the fewest total significant figures. Multiplication and Division Round off the calculated result to the same number of significant figures as the measurement with the fewest total significant figures.

10. Addition / Subtraction 478.34 + 23.987 1. Perform normal mathematical operation 2. Determine how many significant figures the answer should have 3. Round answer to correct number of significant figures 478.34 + 23.987 1. Perform normal mathematical operation 2. Determine how many significant figures the answer should have 3. Round answer to correct number of significant figures 1. 502.327 2. 2 3. 502.33

11. Multiplication & Division 9.7854  2.1 1. Perform normal mathematical operation 2. Determine how many sig. figs. the answer should have. 3. Round the answer to the correct number of sig. figs. 9.7854  2.1 1. Perform normal mathematical operation 2. Determine how many sig. figs. the answer should have. 3. Round the answer to the correct number of sig. figs. 1. 4.659714286 2. 2 3. 4.7

12. Example problems 1. 14.078 - 2.13 2. 0.02 + 0.98734 3. 2.4567 + 135.321 1. 16.020 x 150 2. 0.0422  12 3. 2.65  0.32 1. 14.078 - 2.13 2. 0.02 + 0.98734 3. 2.4567 + 135.321 1. 16.020 x 150 2. 0.0422  12 3. 2.65  0.32 1. 11.95 2. 1.01 3. 137.778 1. 2400 2. 0.0035 3. 0.85

13. Practice Rounding 0.000 345 6 (3) 200.0078 (5) 589.5 (3) 0.003 007 (2) 2 260 000 (4) 0.000 345 6 (3) 200.0078 (5) 589.5 (3) 0.003 007 (2) 2 260 000 (4) 0.000 346 200.01 590. 0.003 0 2.260 x 10 6