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# 2 3 measured_number_and_sig

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### 2 3 measured_number_and_sig

1. 1. <ul><li>2.3 </li></ul><ul><li>Measured Numbers and Significant Figures </li></ul>Chapter 2 Measurements Basic Chemistry Copyright © 2011 Pearson Education, Inc.
2. 2. Measured Numbers <ul><li>A measuring tool </li></ul><ul><li>is used to determine a quantity such as the length or the mass of an object </li></ul><ul><li>provides numbers for a measurement called measured numbers </li></ul>Basic Chemistry Copyright © 2011 Pearson Education, Inc.
3. 3. <ul><li>. l 2 . . . . l . . . . l 3 . . . . l . . . . l 4 . . cm </li></ul><ul><li>The markings on the meterstick at the end of the orange line are read as </li></ul><ul><li>The first digit 2 plus the second digit 2.7 </li></ul><ul><li>The last digit is obtained by estimating. </li></ul><ul><li>The end of the line might be estimated between 2.7–2.8 as half-way (0.05) or a little more (0.06), which gives a reported length of 2.75 cm or 2.76 cm. </li></ul>Reading a Meterstick Basic Chemistry Copyright © 2011 Pearson Education, Inc.
4. 4. Known + Estimated Digits <ul><li>In the length reported as 2.76 cm, </li></ul><ul><li>the digits 2 and 7 are certain ( known ) </li></ul><ul><li>the final digit 6 was estimated ( uncertain ) </li></ul><ul><li>all three digits (2.76) are significant including the estimated digit </li></ul>Basic Chemistry Copyright © 2011 Pearson Education, Inc.
5. 5. Learning Check <ul><li>. l 8 . . . . l . . . . l 9 . . . . l . . . . l 10 . . cm </li></ul><ul><li>What is the length of the red line? </li></ul><ul><li>1) 9.0 cm </li></ul><ul><li>2) 9.03 cm </li></ul><ul><li>3) 9.04 cm </li></ul>Basic Chemistry Copyright © 2011 Pearson Education, Inc.
6. 6. Solution <ul><li>. l 8 . . . . l . . . . l 9 . . . . l . . . . l 10 . . cm </li></ul><ul><li>The length of the red line could be reported as </li></ul><ul><li>2) 9.03 cm </li></ul><ul><li>or 3) 9.04 cm </li></ul><ul><li>The estimated digit may be slightly different. Both readings are acceptable. </li></ul>Basic Chemistry Copyright © 2011 Pearson Education, Inc.
7. 7. <ul><li>. l 3 . . . . l . . . . l 4 . . . . l . . . . l 5 . . cm </li></ul><ul><li>For this measurement, the first and second known digits are 4.5. </li></ul><ul><li>Because the line ends on a mark, the estimated digit in the hundredths place is 0. </li></ul><ul><li>This measurement is reported as 4.50 cm . </li></ul>Zero as a Measured Number Basic Chemistry Copyright © 2011 Pearson Education, Inc.
8. 8. Significant Figures in Measured Numbers <ul><li>Significant figures obtained from a measurement include all of the known digits plus the estimated digit. </li></ul><ul><li>The number of significant figures reported in a measurement depends on the measuring tool. </li></ul>Basic Chemistry Copyright © 2011 Pearson Education, Inc.
9. 9. Significant Figures Basic Chemistry Copyright © 2011 Pearson Education, Inc.
10. 10. <ul><li>All nonzero numbers in a measured number are significant. </li></ul><ul><li>Measurement Number of </li></ul><ul><li>Significant Figures </li></ul><ul><li>38.15 cm 4 </li></ul><ul><li>5.6 ft 2 </li></ul><ul><li>65.6 lb 3 </li></ul><ul><li>122.55 m 5 </li></ul>Counting Significant Figures Basic Chemistry Copyright © 2011 Pearson Education, Inc.
11. 11. <ul><li>Sandwiched zeros </li></ul><ul><li>occur between nonzero numbers </li></ul><ul><li>are significant </li></ul><ul><li>Measurement Number of Significant Figures </li></ul><ul><li>50.8 mm 3 </li></ul><ul><li>2001 min 4 </li></ul><ul><li>0.0702 lb 3 </li></ul><ul><li>0.40505 m 5 </li></ul>Sandwiched Zeros Basic Chemistry Copyright © 2011 Pearson Education, Inc.
12. 12. <ul><li>Trailing zeros </li></ul><ul><li>follow nonzero numbers in numbers without decimal points </li></ul><ul><li>are placeholders </li></ul><ul><li>are not significant </li></ul><ul><li>Measurement Number of Significant Figures </li></ul><ul><li>25 000 cm 2 </li></ul><ul><li>200 kg 1 </li></ul><ul><li>48 600 mL 3 </li></ul><ul><li>25 005 000 g 5 </li></ul>Trailing Zeros Basic Chemistry Copyright © 2011 Pearson Education, Inc.
13. 13. <ul><li>Leading zeros </li></ul><ul><li>precede nonzero digits in a decimal number </li></ul><ul><li>are placeholders </li></ul><ul><li>are not significant </li></ul><ul><li>Measurement Number of Significant Figures </li></ul><ul><li>0.008 mm 1 </li></ul><ul><li>0.0156 oz 3 </li></ul><ul><li>0.0042 lb 2 </li></ul><ul><li>0.000262 mL 3 </li></ul>Leading Zeros Basic Chemistry Copyright © 2011 Pearson Education, Inc.
14. 14. Significant Figures in Scientific Notation <ul><li>In scientific notation </li></ul><ul><li>all digits including zeros in the coefficient are significant </li></ul><ul><li>Scientific Notation Number of </li></ul><ul><li>Significant Figures </li></ul><ul><li>8 x 10 4 m 1 </li></ul><ul><li>8.0 x 10 4 m 2 </li></ul><ul><li>8.00 x 10 4 m 3 </li></ul>Basic Chemistry Copyright © 2011 Pearson Education, Inc.
15. 15. <ul><li>State the number of significant figures in each </li></ul><ul><li>of the following measurements: </li></ul><ul><li>A. 0.030 m </li></ul><ul><li>B. 4.050 L </li></ul><ul><li>C. 0.0008 g </li></ul><ul><li>D. 2.80 m </li></ul><ul><li> </li></ul>Learning Check Basic Chemistry Copyright © 2011 Pearson Education, Inc.
16. 16. <ul><li>State the number of significant figures in each of the </li></ul><ul><li>following measurements: </li></ul><ul><li>A. 0.030 m 2 </li></ul><ul><li>B. 4.050 L 4 </li></ul><ul><li>C. 0.0008 g 1 </li></ul><ul><li>D. 2.80 m 3 </li></ul><ul><li> </li></ul>Solution Basic Chemistry Copyright © 2011 Pearson Education, Inc.
17. 17. <ul><li>A. Which answer(s) contain three significant figures? </li></ul><ul><ul><li>1) 0.4760 2) 0.00476 3) 4.76 x 10 3 </li></ul></ul><ul><li>B. All the zeros are significant in </li></ul><ul><li> 1) 0.00307 2) 25.300 3) 2.050 x 10 3 </li></ul><ul><li>C. The number of significant figures in 5.80 x 10 2 is </li></ul><ul><li> 1) one 3) two 3) three </li></ul>Learning Check Basic Chemistry Copyright © 2011 Pearson Education, Inc.
18. 18. <ul><li>A. Which answer(s) contain three significant figures? </li></ul><ul><ul><li>2) 0.00476 3) 4.76 x 10 3 </li></ul></ul><ul><li>B. All the zeros are significant in </li></ul><ul><li>2) 25.300 3) 2.050 x 10 3 </li></ul><ul><li>C. The number of significant figures in 5.80 x 10 2 </li></ul><ul><li>is </li></ul><ul><li>3) three </li></ul>Solution Basic Chemistry Copyright © 2011 Pearson Education, Inc.
19. 19. <ul><li>In which set(s) do both numbers contain the </li></ul><ul><li>same number of significant figures? </li></ul><ul><li>1) 22.0 and 22.00 </li></ul><ul><li>2) 400.0 and 4.00 x 10 2 </li></ul><ul><li>3) 0.000015 and 150 000 </li></ul>Learning Check Basic Chemistry Copyright © 2011 Pearson Education, Inc.
20. 20. Solution <ul><li>In which set(s) do both numbers contain the </li></ul><ul><li>same number of significant figures? </li></ul><ul><li> 3) 0.000015 and 150 000 </li></ul><ul><li>Both numbers contain two (2) significant </li></ul><ul><li>figures. </li></ul>Basic Chemistry Copyright © 2011 Pearson Education, Inc.
21. 21. Exact Numbers <ul><li>An exact number is obtained </li></ul><ul><li>when objects are counted </li></ul><ul><li>Example : counting objects </li></ul><ul><ul><li>2 baseballs </li></ul></ul><ul><ul><li>4 pizzas </li></ul></ul><ul><li>from numbers in a defined relationship </li></ul><ul><li>Example : defined relationships </li></ul><ul><ul><li>1 foot = 12 inches </li></ul></ul><ul><ul><li>1 meter = 100 cm </li></ul></ul>Basic Chemistry Copyright © 2011 Pearson Education, Inc.
22. 22. Examples of Exact Numbers Basic Chemistry Copyright © 2011 Pearson Education, Inc.
23. 23. Learning Check <ul><li>A. Exact numbers are obtained by </li></ul><ul><li> 1. using a measuring tool </li></ul><ul><li> 2. counting </li></ul><ul><li> 3. definition </li></ul><ul><li>B. Measured numbers are obtained by </li></ul><ul><li> 1. using a measuring tool </li></ul><ul><li> 2. counting </li></ul><ul><li> 3. definition </li></ul>Basic Chemistry Copyright © 2011 Pearson Education, Inc.
24. 24. Solution <ul><li>A. Exact numbers are obtained by </li></ul><ul><li> 2. counting </li></ul><ul><li> 3. definition </li></ul><ul><li>B. Measured numbers are obtained by </li></ul><ul><li> 1. using a measuring tool </li></ul>Basic Chemistry Copyright © 2011 Pearson Education, Inc.
25. 25. Learning Check <ul><li>Classify each of the following as exact (E) or </li></ul><ul><li>measured numbers (M). Explain your answer. </li></ul><ul><li>A.__Gold melts at 1064 °C. </li></ul><ul><li>B.__1 yd = 3 ft </li></ul><ul><li>C.__The diameter of a red blood cell is 6 x 10  4 cm. </li></ul><ul><li>D.__There are 6 hats on the shelf. </li></ul><ul><li>E.__A can of soda contains 355 mL of soda. </li></ul><ul><li> </li></ul>Basic Chemistry Copyright © 2011 Pearson Education, Inc.
26. 26. <ul><li>Classify each of the following as exact (E) or </li></ul><ul><li>measured numbers (M) . </li></ul><ul><li>A. M A measuring tool is required. </li></ul><ul><li>B. E This is a defined relationship. </li></ul><ul><li>C. M A measuring tool is used to determine </li></ul><ul><li> length. </li></ul><ul><li>D. E The number of hats is obtained by counting. </li></ul><ul><li>E. M The volume of soda is measured. </li></ul>Solution Basic Chemistry Copyright © 2011 Pearson Education, Inc.