Significant Figures There are two kinds of numbers

Significant Figures

There are two kinds of numbers: n Exact Example: There are twelve eggs in a dozen n Inexact Example: Any measurment

Which of the following would be exact numbers? The elevation of Breckinridge, Colorado (9600 ft) OR n The announced attendance at a football game (87, 451) n War Eagle!

If I were to measure a piece of paper… I might get 20. 15 mm n You might get 20. 14 mm n Somebody else may get 20. 16 mm n Who is right ? ? ?

Precision vs. Accuracy n Accuracy -Refers to how closely a measured value agrees with the correct value n Precision -Refers to how closely individual measurements agree with each other

Describe the following in terms of precision and/or accuracy… Scenario #1: A chemistry student uses a graduated cylinder to measure the volume of a liquid and found the measurement to be 20. 1 m. L. The actual measurement was 27. 3 m. L. n The student’s measurement was not accurate.

Describe the following in terms of precision and/or accuracy… n Scenario #2: A man practices his dart throws in attempt to hit the bulls-eye! Here are his results: These darts were both precise and accurate. One dart was accurate. The rest of the darts were inaccurate. The darts were not precise either.

Remember… There is uncertainty in all measurement, but the precision is determined by the measuring device. In any measurement, the number of significant figures is the number of digits believed to be correct by the person doing the measuring ***It also includes one estimated digit.

A rule of thumb: Volumes should be read to 1/10 of the smallest division. Example: If the smallest division is 10 m. L, the volume would be read as having an error of 1 m. L.

A Beaker n n The smallest division is 10 m. L-so we can read the volume to 1 m. L. The volume in the beaker is 47(+ or –) 1 m. L. It might be 46 m. L or it might be 48 m. L. So, how many sig. figs. ? ? (2) - The “ 4” we know for sure, plus the “ 7” that we had to estimate.

A Graduated Cylinder n n n The smallest division is 1 m. L so we can read the volume to 0. 1 m. L. The volume could be read as 36. 5 (+ or -) 0. 1 m. L. The true volume could be 36. 4 m. L or 36. 6 m. L. How many sig. figs? ? ? (3) - The “ 3” and “ 6” we know for sure. The “ 5” had to be estimated.

A Buret n n n The smallest division is 0. 1 m. L so we can read the volume to 0. 01 m. L. A good volume reading would be 20. 62 (+ or -) 0. 01 m. L. An equally precise answer would be 20. 61 m. L or 20. 63 m. L. How many sig. figs. ? ? (4) - The “ 2”, “ 0”, and “ 6” we know for sure, the last “ 2” we had to estimate.

Conclusion: Significant figures are directly linked with measurement.

Determining the number of sig. figs. in a number n n Picture a map of the U. S…. If a decimal point is present in a number, count from the Pacific side. Start counting with the first nonzero digit. All digits from here to the end, including zeros, are significant.

Examples: v 0. 00682 Answer: 3 v 1. 0 Answer: 2 v 60. Answer: 2 v 1. 0 x 102 Answer: 2

n If the decimal point is absent, start counting from the Atlantic side. n Start with the first nonzero digit. n All digits from here to the end, including zeros, are significant.

Examples: v 60 Answer: 1 v 603 Answer: 3 v 6030 Answer: 3

Significant Figures in Calculations: Rules for Multiplication and Division The answer contains no more significant figures than the least accurately known number.

Examples: The number with the least # of sig. figs. has 2 sig. figs. Therefore, the answer must have 2. The number with the least # of sig. figs. has 3 sig. figs. Therefore, the answer must have 3.

Practice! Calculate and answer using the correct number of sig figs. 145 x 29 n 4205 4200 n 118. 2 x 10. 4 n 1229. 28 1230 n 1. 245 x 3. 9 n 4. 8555 4. 9 n 12. 9 / 3. 4 n 3. 79 3. 8 n 38 / 6. 435 n 5. 90 5. 9 n 23. 245 / 6. 917 n 3. 36056 3. 361 n

Rules for Addition and Subtraction The number of sig. figs. is determined by the location of digits in the number with the largest uncertainty, not the number of significant figures in the number.

Examples: The least precise # is 2. 02. It has sig. figs. out to the hundredths place. Therefore the answer will have sig. figs. out to the hundredths place. The least precise # 1. 0236 has decimals carried out 4 places. Therefore the answer will have sig. figs. carried out 4 decimal places.

Practice! Calculate and answer using the correct number of sig figs. 14. 51 + 29. 2 n 43. 71 43. 7 n 1. 2 + 10. 498 n 11. 698 11. 7 n 1 + 3. 9 n 4. 9 5 n 12. 94 - 3. 4 n 9. 54 9. 5 n 38 – 6. 435 n 31. 565 32 n 23. 2 - 6. 917 n 16. 283 16. 3 n