1. Working with Significant Figures

2. Exact Numbers Some numbers are exact, either because: We count them (there are 14 elephants) By definition (1 inch = 2.54 cm) These numbers have no limit of significant digits For the rest of our measurements and calculations, we need to keep track of Sig Figs!

3. Significant Figures RULE #1 Include ONE estimated digit 5.2 cm

4. Sig Fig Rule #2 Count all non-zero integers: 452 (3 sig figs) 59,294 (5 sig figs) 28 (2 sig figs) 893,438,894 (9 sig figs)

5. Sig Fig Rule #3 Any zeros coming before all the non- zero digits don’t count: 0.67291 (5 sig figs) 0.00239 (3 sig figs) 0.00004 (1 sig fig)

6. Sig Fig Rule #4 DO count any zeros trapped between non-zero digits: 5.0031 (5 sig figs) 80,045 (5 sig figs) 0.3906 (4 sig figs) 0.004900302 (7 sig figs)

7. Sig Fig Rule # 5 Count zeros to the right of all non-zero digits only if there is a decimal: 6.300 (4 sig figs) 470.00 (5 sig figs) 200 (1 sig fig) 200. (3 sig figs)

8. The Chart Tape this into your Lab Journal for your reference and practice.

9. Some Practice Give the number of significant figures for each example a)8.9007 b)5,000 c)0.0396 d)10,700. e)0.2000 f)7.003051 g)0.00175 h)4,602,390 i)0.000300 j)60

10. Calculating with Significant Figures When we do math with these numbers, always round to the number of significant figures represented by the most uncertain number. There are rules, depending on the operations you perform.

11. Calculating with Significant Figures: Multiplication & Division Sig figs in answer = Sig figs in the term with the smallest number of Sig figs, because that is the least accurate measurement.

12. Multiplication Example: ➡ 4.56 x 1.4 = 6.384 ➡ 4.56 has three significant figures and 1.4 has two significant figures, therefore round off to two significant figures in your answer = 6.4

13. Division Example: ➡ Example: 8.315 = 0.0279027 298 ➡ Since 298 has the least number of significant figures (3), we round the answer to 0.0279

14. Multiplication & Division Practice a) 14 x 0.8725 b) 2,096 x 1.3 c) 47,249 x 0.0035 d) 38,000 x 2.72046 e) 536 x 0.000012 f) 67.90 ÷ 2 g) 5600 ÷0.368 h) 884.00÷76. i) 0.0082 ÷ 1.6115

15. Calculating with Significant Figures: Addition & Subtraction Sig Figs in answer = the term with the fewest decimal places. Use that many decimal places in your answer.

16. Addition Example: ➡ Example: 12.11 18.0 Since 18.0 has just one + 1.013 decimal place, we will 31.123 round off the answer to one decimal place. = 31.1

17. Addition & Subtraction Practice a) 78.50 +6.2106 b) 142.0917 – 3, c) 400. – 1.43 (d) 62.55 143.1 + 0.21060 (e) 1.0917 127.00.716 + 35.7,

18. Rounding Off Once you have determined how many significant figures is in your answer, there are a few rules for rounding off: 1. Round down if the digit to be removed is less than 5. 1.33 rounded to two significant figures becomes 1.3 2. Round up if the digit to be removed is 5 or greater. Rounding to two significant figures, 1.36 becomes 1.4 and 3.15 becomes 3.2. 3. If you are removing a string of numbers, only look at the first number to the right. Rounding 4.348 to two significant figures becomes 4.3. 4. In a series of calculations, keep the extra digits until your final result, then round.

19. Homework Significant Figures Practice