1. End Show © Copyright Pearson Prentice Hall Measurements and Their Uncertainty > Slide 1 of 48 Significant Figures in Calculations Significant Figures in Addition and Subtraction Calculations 3.1

2. End Show © Copyright Pearson Prentice Hall Measurements and Their Uncertainty > Slide 2 of 48 3.1 Significant Figures in Calculations ***Rules for determining number of SF in final answer when Adding or Subtracting do the mathematical operation the value with the least number of decimal places in the original data determines the place of the last sig fig in the answer. Round appropriately to report final answer Convert to scientific notation if needed

3. End Show © Copyright Pearson Prentice Hall Measurements and Their Uncertainty > Slide 3 of 48 C. Significant Figures  67.9 mL  28.29 g 63.75 mL + 4.1 mL 32.587 g - 4.30 g 67.85 mL 28.287 Ex. 1 Try this:

4. End Show © Copyright Pearson Prentice Hall SAMPLE PROBLEM Slide 4 of 48 Always re-write to line up the decimal 12.52 349.0 8.24 369.76 do the math ANS: 369.8 m just for fun…write in scientific notation 3.698 x 10 2 m Least number of decimal places Round correctly ****SigFigs in standard or scientific must always be the same but decimal places do not have to be the same!!!!!******

5. End Show © Copyright Pearson Prentice Hall Measurements and Their Uncertainty > Slide 5 of 48 C. Significant Figures  1150 g 924 g + 230 g  1.15 x 10 3 g If values you are adding or subtracting, don’t have decimal points, the least accurate number determines the number of SF in the final answer 1154 g Ex. 2 Notice, rules for adding sf determined: 3 sig figs and no decimal point But, rules for converting from standard to SN determined: just keep total number of SF the same and do not worry about decimal places!

6. End Show © Copyright Pearson Prentice Hall SAMPLE PROBLEM Slide 6 of 48 write each number so the exponents are identical re-write to line up the decimal do the mathematical operation round to correct number of sig figs put final answer in correct scientific notation Example: 3.75 x 10 -5 m + 7.00 x 10 -5 m 3.75 x 10 -5 + 7.00 x 10 -5 10.75 x 10 -5 round to the least number of decimal places 10.75 x 10 -5 Write in proper scientific notation (b/c original given in sn) ANS: 1.075 x 10 -5 m (notice different number of decimal places!!!) Adding and Subtracting w/ Scientific Notation

7. End Show © Copyright Pearson Prentice Hall SAMPLE PROBLEM Slide 7 of 48 Try this: 3.6 x 10 -5 m + 6.5 x 10 -4 m Convert to the same exponent and re-write with decimals lined up. 36 x 10 -4 3.6 x 10 -5 + 6. 5 x 10 -4 + 65. x 10 -5 6. 86 x 10 -4 68.6 x 10 -5 6.9 x 10 -4 m or 69 x 10 -5 ans: 6.9 x 10 -4 m

8. End Show © Copyright Pearson Prentice Hall SAMPLE PROBLEM Slide 8 of 48 PRACTICE PROBLEMS in packet