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Understanding Significant Figures in Measurements

Explore the concept of significant figures in measurements, including rules for exact numbers and rounding off, with examples and scientific notation explained.

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Understanding Significant Figures in Measurements

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  1. Chem 160- Ch # 2l. Numbers from measurements.

  2. Measurements • Experiments are performed. • Numerical values or data are obtained from these measurements.

  3. Exact Numbers • Exact numbers have an infinite number of significant figures. • Exact numbers occur in simple counting operations 1 2 3 4 5 • Defined numbers are exact. 12 inches = 1 foot 100 centimeters = 1 meter

  4. numerical value 70.0 kilograms = 154 pounds unit Form of a Measurement

  5. known estimated Significant Figures • The number of digits that are known plus one estimated digit are considered significant in a measured quantity 5.16143

  6. Significant Figures on Reading a Thermometer

  7. The temperature 21.2oC is expressed to 3 significant figures. Temperature is estimated to be 21.2oC. The last 2 is uncertain.

  8. The temperature 22.0oC is expressed to 3 significant figures. Temperature is estimated to be 22.0oC. The last 0 is uncertain.

  9. The temperature 22.11oC is expressed to 4 significant figures. Temperature is estimated to be 22.11oC. The last 1 is uncertain.

  10. Significant Figures All nonzero numbers are significant. 461

  11. Significant Figures All nonzero numbers are significant. 461

  12. Significant Figures All nonzero numbers are significant. 3 Significant Figures 461

  13. Significant Figures A zero is significant when it is between nonzero digits. 3 Significant Figures 401

  14. Significant Figures A zero is significant when it is between nonzero digits. 5 Significant Figures 9 3 . 0 0 6

  15. Significant Figures A zero is significant at the end of a number that includes a decimal point. 5 Significant Figures 5 5 . 0 0 0

  16. Significant Figures A zero is significant at the end of a number that includes a decimal point. 5 Significant Figures 2 . 1 9 3 0

  17. Significant Figures A zero is not significant when it is before the first nonzero digit. 1 Significant Figure 0 . 0 0 6

  18. Significant Figures A zero is not significant when it is before the first nonzero digit. 3 Significant Figures 0 . 7 0 9

  19. Significant Figures A zero is not significant when it is at the end of a number without a decimal point. 1 Significant Figure 5 0 0 0 0

  20. Roundingoff Numbers

  21. Rounding Off Numbers • Often when calculations are performed extra digits are present in the results. • It is necessary to drop these extra digits so as to express the answer to the correct number of significant figures. • When digits are dropped the value of the last digit retained is determined by a process known as rounding off numbers.

  22. Rounding Off Numbers Rule 1. When the first digit after those you want to retain is 4 or less, that digit and all others to its right are dropped. The last digit retained is not changed. 4 or less 80.873

  23. 5 or greater drop these figures Rounding Off Numbers Rule 2. When the first digit after those you want to retain is 5 or greater, that digit and all others to its right are dropped. The last digit retained is increased by 1. increase by 1 5.459672 6

  24. Significant Figures in Calculations

  25. Multiplication or Division

  26. In multiplication or division, the answer must contain the same number of significant figures as in the measurement that has the least number of significant figures.

  27. Drop these three digits. 2.3 has two significant figures. (190.6)(2.3) = 438.38 190.6 has four significant figures. Answer given by calculator. The answer should have two significant figures because 2.3 is the number with the fewest significant figures. Round off this digit to four. 438.38 The correct answer is 440 or 4.4 x 102

  28. Addition or Subtraction

  29. The results of an addition or a subtraction must be expressed to the same precision as the least precise measurement.

  30. The result must be rounded to the same number of decimal places as the value with the fewest decimal places.

  31. 125.17 129. 52.2 Add 125.17, 129 and 52.2 Least precise number. Answer given by calculator. 306.37 Round off to the nearest unit. Correct answer. 306.37

  32. Scientific Notation of Numbers

  33. Very large and very small numbers are often encountered in science. 602200000000000000000000 0.00000000000000000000625 • Very large and very small numbers like these are awkward and difficult to work with.

  34. 6.25 x 10-21 A method for representing these numbers in a simpler form is called scientific notation. 6.022 x 1023 602200000000000000000000 0.00000000000000000000625

  35. Scientific Notation • Write a number as a power of 10 • Move the decimal point in the original number so that it is located after the first nonzero digit. • Follow the new number by a multiplication sign and 10 with an exponent (power). • The exponent is equal to the number of places that the decimal point was shifted.

  36. Write 6419 in scientific notation. decimal after first nonzero digit power of 10 6.419 x 103 64.19x102 641.9x101 6419. 6419

  37. Write 0.000654 in scientific notation. decimal after first nonzero digit power of 10 6.54 x 10-4 0.000654 0.00654 x 10-1 0.0654 x 10-2 0.654 x 10-3

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