1. Significant Figures When we take measurements or make calculations, we do so with a certain precision. This precision is determined by the instrument we use to take those measurements. So, when we do calculations based on our measurements, the calculations must be as precise as the measurements.

2. Rules: How to determine how many significant figures (ie. How precise?) • All numbers between 1 and 9 (non-zero) are always significant. • Zeros between 2 non-zero numbers are always significant. • Example: 234.7 4 significant figures 2008 4 sig. figs. 200.8 4 sig. figs. 23.47 4 sig. figs.

3. All numbers after (to the right) of the decimal are significant. 2.89 3 sig. figs. 2.00 3 sig. figs. 2.0 2 sig. figs. 2.0004 5 sig. figs. • Any zeros before the decimal are not significant. 0.345 3 sig. figs. 0.230 3 sig. figs.

4. Zeros that serve to indicate the position of the decimal are not significant. 2300 2 sig. figs. 100 1 sig. fig. These 2 numbers indicate 23 hundred and 1 hundred. If there was a decimal at the end of these numbers, it would change the precision and therefore change the number of significant figures. 2300. 4 sig. figs. 100. 3 sig. figs.

5. Problems: Indicate the number of significant figures... 1. 1.235 ______ 2. 2.90 ______ 3. 0.0987 ______ 4. 0.450 ______ 5. 5.00 ______ 6. 2300 ______ 7. 230 ______ 8. 230.0 ______ 9. 9870345 ______ 10. 1.00000 ______

6. Adding and subtracting with Sig. Figs. • The last sig fig in a measurement is an estimate (not known with certainty). Measurements can only have one estimated digit. • The answer, when you add or subtract, can not be better than your worst estimate. • You have to round the answer to the place value of the measurement (in the problem) with the greatest uncertainty.

7. 27.93 + 6.4 27.93 27.93 + 6.4 6.4 For example • First line up the decimal places Then do the adding Find the estimated numbers in the problem 34.33 This answer must be rounded to the tenths place

8. Rules for addition and subtraction: • Determine which number has the least amount of significant figures after the decimal. 26.24 + 4.1245 = 30. 5645 answer =30.56 26.46- 4.2= 22. 26 answer = 22.3

9. Problems: addition and subtraction 1. 2.634 + 0.02 ______ 2. 2.634 - 0.02 ______ 3. 230 + 50.0 ______ 4. 0.034 + 1.00 ______ 5. 4.56 - 0.34 ______ 6. 3.09 - 2.0 ______ 7. 349 + 34.09 ______ 8. 234 - 0.98 ______ 9. 238 + 0.98 ______ 10. 123.98 + 0.54 - 2.3 ______

10. MULTIPLICATION and DIVISION

11. Multiplication and division 1.Determine which number has the least amount of significant figures in total. This is the number of significant figures your answer will have. 2.61 x 1.2 = 3.132 2.61 ÷ 1.2 = 2.175 answer = 3.1 answer = 2.2 ***sometimes you have to “round-off”!!

12. Rounding rules • Look at the digit in the place value following the one you’re rounding. • If the first digit to be cut is 0 to 4 don’t change it (round down) • If the first digit to be cut is 6 to 9 make it one bigger (round up) • If the first digit to be cut is exactly 5 (followed by nothing or zeros), round the number so that the preceding digit will be even. • Round 45.462 cm to: four sig figs to three sig figs to two sig figs to one sig fig 45.46 cm 45.5 cm 46 cm 50 cm

13. Problems: multiplication & division 1. 42.3 x 2.61 ______ 2. 32.99 x 0.23 ______ 3. 46.1 ÷ 1.21 ______ 4. 23.3 ÷ 4.1 ______ 5. 0.61 x 42.1 ______ 6. 47.2 x 0.02 ______ 7. 47.2 ÷ 0.023 ______ 8. 100 x 23 ______ 9. 120 ÷ 0.12 ______ 10. 120 x 12 ÷ 12.5 ______