Chapter 1 Measurements <ul><li>Measured Numbers and Significant Figures </li></ul>
Measured Numbers <ul><li>When you use a measuring tool is used to determine a quantity such as your height or weight, the ...
Reading a Meterstick <ul><li>.  l 2 . . . . I . . . . I 3  . . . .I . . . . I 4 . .  cm </li></ul><ul><li>First digit (kno...
Known + Estimated Digits <ul><li>Known digits  2  and  7  are 100% certain </li></ul><ul><li>The third digit 6 is estimate...
Learning Check <ul><li>. l 8 . . . . I . . . . I 9 . . . .I . . . . I 10 . .  cm </li></ul><ul><li>What is the length of t...
Solution <ul><li>. l 8 . . . . I . . . . I 9 . . . .I . . . . I 10 . .  cm </li></ul><ul><li>Estimate to the hundreth’s pl...
Learning Check <ul><li>l 5 . . . . I . . . . I 6 . . . .I . . . . I 7 . .  cm </li></ul><ul><li>What is the length of the ...
Solution  <ul><li>l 5 . . . . I . . . . I 6 . . . .I . . . . I 7 . .  cm </li></ul><ul><li>Estimate to the hundreth’s plac...
Zero as a Measured Number <ul><li>. l 3 . . . . I . . . . I 4  . . . . I . . . . I 5 . .  cm </li></ul><ul><li>What is the...
Exact Numbers <ul><li>Obtained when you count objects </li></ul><ul><ul><li>2 soccer balls </li></ul></ul><ul><ul><li>1 wa...
Learning Check  <ul><li>A.  Exact numbers are obtained by </li></ul><ul><li>  1.  measuring   </li></ul><ul><li>2.  counti...
Solution  <ul><li>A.  Exact numbers are obtained by </li></ul><ul><li>  2.  counting </li></ul><ul><li>3.  definition </li...
Learning Check  <ul><li>Classify each of the following as an exact  (1)  </li></ul><ul><li>or a  measured  (2)  number. </...
Solution  <ul><li>Classify each of the following as an exact (1) or a  measured(2) number.  Give reason. </li></ul><ul><li...
% Yield <ul><li>Actual/Theoretical x 100% </li></ul><ul><li>If you are attempting an experiment and the theoretical yield ...
 
Variables <ul><li>Independent Variable: </li></ul><ul><li>A variable that stands alone and is not changed. Not changed by ...
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Measured And Exact Numbers

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Measured And Exact Numbers

  1. 1. Chapter 1 Measurements <ul><li>Measured Numbers and Significant Figures </li></ul>
  2. 2. Measured Numbers <ul><li>When you use a measuring tool is used to determine a quantity such as your height or weight, the numbers you obtain are called measured numbers . </li></ul>
  3. 3. Reading a Meterstick <ul><li>. l 2 . . . . I . . . . I 3 . . . .I . . . . I 4 . . cm </li></ul><ul><li>First digit (known) = 2 2 .?? cm </li></ul><ul><li>Second digit (known) = 0 .7 2.7 ? cm </li></ul><ul><li>Third digit (estimated) between 0.05- 0.07 </li></ul><ul><li>Length reported = 2.75 cm </li></ul><ul><li> or 2.76 cm </li></ul><ul><li>or 2.77 cm </li></ul>
  4. 4. Known + Estimated Digits <ul><li>Known digits 2 and 7 are 100% certain </li></ul><ul><li>The third digit 6 is estimated (uncertain) </li></ul><ul><li>In the reported length, all three digits </li></ul><ul><li>(2.76 cm) are significant including the estimated one </li></ul>
  5. 5. Learning Check <ul><li>. l 8 . . . . I . . . . I 9 . . . .I . . . . I 10 . . cm </li></ul><ul><li>What is the length of the line? </li></ul><ul><li>1) 9.2 cm </li></ul><ul><li>2) 9.22 cm </li></ul><ul><li>3) 9.23 cm </li></ul><ul><li>How your answer compare with your neighbor’s answer? Why or why not? </li></ul>
  6. 6. Solution <ul><li>. l 8 . . . . I . . . . I 9 . . . .I . . . . I 10 . . cm </li></ul><ul><li>Estimate to the hundreth’s place (0.01 cm) </li></ul><ul><li>2) 9.22 cm </li></ul><ul><li>3) 9.23 cm </li></ul><ul><li>The estimated digit may be slightly different. Both readings are acceptable. </li></ul>
  7. 7. Learning Check <ul><li>l 5 . . . . I . . . . I 6 . . . .I . . . . I 7 . . cm </li></ul><ul><li>What is the length of the line? </li></ul><ul><li>1) 6.0 cm </li></ul><ul><li>2) 6.06 cm </li></ul><ul><li>3) 6.60 cm </li></ul>
  8. 8. Solution <ul><li>l 5 . . . . I . . . . I 6 . . . .I . . . . I 7 . . cm </li></ul><ul><li>Estimate to the hundreth’s place (0.01 cm). The reading is between 6.0 and 6.1. You may have estimated 6.07 cm as well. </li></ul><ul><li>2) 6.06 cm </li></ul>
  9. 9. Zero as a Measured Number <ul><li>. l 3 . . . . I . . . . I 4 . . . . I . . . . I 5 . . cm </li></ul><ul><li>What is the length of the line? </li></ul><ul><li>First digit 4.?? cm </li></ul><ul><li>Second digit 4 .5? cm </li></ul><ul><li>Last (estimated) digit is 4.5 0 cm </li></ul><ul><li>(not to the left or right of .5) </li></ul>
  10. 10. Exact Numbers <ul><li>Obtained when you count objects </li></ul><ul><ul><li>2 soccer balls </li></ul></ul><ul><ul><li>1 watch </li></ul></ul><ul><ul><li>4 pizzas </li></ul></ul><ul><li>Obtained from a defined relationship </li></ul><ul><ul><li>1 foot = 12 inches </li></ul></ul><ul><ul><li>1 meters = 100 cm </li></ul></ul><ul><li>Not obtained with measuring tools </li></ul>
  11. 11. Learning Check <ul><li>A. Exact numbers are obtained by </li></ul><ul><li> 1. measuring </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. measuring </li></ul><ul><li>2. counting </li></ul><ul><li>3. definition </li></ul>
  12. 12. 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>
  13. 13. Learning Check <ul><li>Classify each of the following as an exact (1) </li></ul><ul><li>or a measured (2) number. </li></ul><ul><li>A.___Gold melts at 1064°C </li></ul><ul><li>B.___1 yard = 3 feet </li></ul><ul><li>C.___A red blood cell with diameter 6 x 10 -4 cm </li></ul><ul><li>D.___There were 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>
  14. 14. Solution <ul><li>Classify each of the following as an exact (1) or a measured(2) number. Give reason. </li></ul><ul><li>A. 2 Requires a thermometer(measuring tool) </li></ul><ul><li>B. 1 From a definition in U.S. system </li></ul><ul><li>C. 2 Need measuring tool to determine </li></ul><ul><li>D. 1 Counted the hats </li></ul><ul><li>E. 2 Measured </li></ul>
  15. 15. % Yield <ul><li>Actual/Theoretical x 100% </li></ul><ul><li>If you are attempting an experiment and the theoretical yield is 100g and your group’s yield is 79g, determine the % error. </li></ul>
  16. 17. Variables <ul><li>Independent Variable: </li></ul><ul><li>A variable that stands alone and is not changed. Not changed by what we measure. </li></ul><ul><li>Dependent Variable: </li></ul><ul><li>Depends on other factors. This is what changes in the experiment. </li></ul>

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