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# 2 4 significant_fig_in_calc

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### 2 4 significant_fig_in_calc

1. 1. Chapter 2 Measurements <ul><li>2.4 </li></ul><ul><li>Significant Figures in </li></ul><ul><li> Calculations </li></ul>Basic Chemistry Copyright © 2011 Pearson Education, Inc.
2. 2. Rounding Off Answers <ul><li>In calculations </li></ul><ul><li>answers must have the same number of significant figures as the measured numbers </li></ul><ul><li>calculated answers are usually rounded off </li></ul><ul><li>rounding rules are used to obtain the correct number of significant figures </li></ul>Basic Chemistry Copyright © 2011 Pearson Education, Inc.
3. 3. Rounding Off Calculated Answers <ul><li>When the first digit dropped is 4 or less , the retained numbers remain the same. </li></ul><ul><li>to round off 45.832 to 3 significant figures </li></ul><ul><li> drop the digits 32 = 45.8 </li></ul><ul><li>When the first digit dropped is 5 or greater , the last retained digit is increased by 1. </li></ul><ul><li> to round off 2.4884 to 2 significant figures </li></ul><ul><li> drop the digits 884 = 2.5 ( increase by 0.1) </li></ul>Basic Chemistry Copyright © 2011 Pearson Education, Inc.
4. 4. Adding Significant Zeros <ul><li>Sometimes a calculated answer requires more significant digits. Then one or more zeros are added . </li></ul><ul><li>Calculated Zeros Added to </li></ul><ul><li>Answer Give 3 Significant Figures </li></ul><ul><li> 4 4.00 </li></ul><ul><li> 1.5 1.50 </li></ul><ul><li> 0.2 0.200 </li></ul><ul><li>12 12.0 </li></ul>Basic Chemistry Copyright © 2011 Pearson Education, Inc.
5. 5. Learning Check <ul><li>Adjust the following calculated answers to give </li></ul><ul><li>answers with three significant figures: </li></ul><ul><li>A. 824.75 cm </li></ul><ul><li>B. 0.112486 g </li></ul><ul><li>C. 8.2 L </li></ul>Basic Chemistry Copyright © 2011 Pearson Education, Inc.
6. 6. Solution <ul><li>Adjust the following calculated answers to give </li></ul><ul><li>answers with three significant figures: </li></ul><ul><li>A. 825 cm first digit dropped is greater than 5 </li></ul><ul><li>B. 0.112g first digit dropped is 4 </li></ul><ul><li>C. 8.20 L significant zero added </li></ul>Basic Chemistry Copyright © 2011 Pearson Education, Inc.
7. 7. Calculations with Measured Numbers <ul><li>In calculations with measured numbers, significant figures or decimal places are used to determine the correct number of figures in the final answer. </li></ul>Basic Chemistry Copyright © 2011 Pearson Education, Inc.
8. 8. <ul><li>When multiplying or dividing , use </li></ul><ul><li>the same number of significant figures (SFs) as in the measurement with the fewest significant figures </li></ul><ul><li>rounding rules to obtain the correct number of significant figures </li></ul><ul><li>Example </li></ul><ul><li>110.5 x 0.048 = 5.304 = 5.3 (rounded) </li></ul><ul><li>4 SFs 2 SFs calculator 2 SFs </li></ul>Multiplication and Division Basic Chemistry Copyright © 2011 Pearson Education, Inc.
9. 9. <ul><li>Give an answer for each with the correct </li></ul><ul><li>number of significant figures. </li></ul><ul><li>A. 2.19 x 4.2 = </li></ul><ul><li> 1) 9 2) 9.2 3) 9.198 </li></ul><ul><li>B. 4.311 ÷ 0.07 = </li></ul><ul><li> 1) 61.59 2) 62 3) 60 </li></ul><ul><li>C. 2.54 x 0.0028 = </li></ul><ul><li> 0.0105 x 0.060 </li></ul><ul><li> 1) 11.3 2) 11 3) 0.041 </li></ul>Learning Check Basic Chemistry Copyright © 2011 Pearson Education, Inc.
10. 10. <ul><li>A. 2.19 x 4.2 = 2) 9.2 </li></ul><ul><li>B. 4.311 ÷ 0.07 = 3) 60 </li></ul><ul><li>C. 2.54 x 0.0028 = 2) 11 </li></ul><ul><li>0.0105 x 0.060 </li></ul><ul><li> </li></ul><ul><li>On a calculator, enter each number followed by </li></ul><ul><li>the operation key. </li></ul><ul><li>2.54 x 0.0028  0.0105  0.060 = 11.28888889 </li></ul><ul><li>= 11 ( rounded off ) </li></ul>Solution Basic Chemistry Copyright © 2011 Pearson Education, Inc.
11. 11. <ul><li>When adding or subtracting , use </li></ul><ul><li>the same number of decimal places as the measurement with the fewest decimal places </li></ul><ul><li>rounding rules to adjust the number of digits in the answer </li></ul><ul><li> 25.2 one decimal place </li></ul><ul><li> + 1.34 two decimal places </li></ul><ul><li> 26.54 calculated answer </li></ul><ul><li> 26.5 final answer (one decimal place) </li></ul>Addition and Subtraction Basic Chemistry Copyright © 2011 Pearson Education, Inc.
12. 12. <ul><li>For each calculation, round the answer to give </li></ul><ul><li>the correct number of digits. </li></ul><ul><li>A. 235.05 + 19.6 + 2 = </li></ul><ul><li>1) 257 2) 256.7 3) 256.65 </li></ul><ul><li>B. 58.925 - 18.2 = </li></ul><ul><li>1) 40.725 2) 40.73 3) 40.7 </li></ul>Learning Check Basic Chemistry Copyright © 2011 Pearson Education, Inc.
13. 13. <ul><li>A. 235.05 hundredths place (2 decimal places) </li></ul><ul><li>+19.6 tenths place (1 decimal place) </li></ul><ul><li>+ 2 ones place </li></ul><ul><li>256.65 rounds to 257 answer (1) </li></ul><ul><li>B. 58.925 thousandths place (3 decimal places) </li></ul><ul><li>-18.2 tenths place (1 decimal place) </li></ul><ul><li> 40.725 round to 40.7 answer (3) </li></ul>Solution Basic Chemistry Copyright © 2011 Pearson Education, Inc.