06 significant figures

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06 significant figures

  1. 1. Significant Figures
  2. 2. Why Significant Figures  It enables us to have a clear idea of the extent of the precision of the measuring instrument being used or the measuring method being employed.
  3. 3. Which figures are significant?  Rule #1: Non-zero digits are always significant  Rule #2: All zeroes between significant digits are significant  Rule #3: A final zero or trailing zeroes can only be significant if there is a decimal point or a bar. Let’s practice! 1234 kg 56, 789 ft 101 hr 134.001 kW 1230909 cm 10.0 s 100. s $ 2050.00 7000 kW 0.0204000
  4. 4. Which figures are NOT significant?  Zeroes are usually not significant in the following instances:  Leading zeroes: zeroes before any significant figure are never significant.  Ex. 0056, 0.00108  Trailing zeroes: zeroes after any significant figure are not significant when there are no decimal points or bars  Ex. 76 000, 76 000., 76 00.0, 0.076000, 76
  5. 5. Infinite Number of Significant Figures  Counted Numbers  12 eggs in a dozen  There are 16 students in a class  Physical Constants  The value of π (3.14)  Avogadros’ Constant 6.02 x 1023
  6. 6. Seatwork: How many significant figures? 1. 600. 2. 2.090 3. 4. 5. 6. 0 3045 0.001 0 0.056 0 0.009 9 8. 0.0300 9. 0.0080 10.10 006 11.0.003 30 12.0.070 0 13.2 900
  7. 7. Seatwork: How many significant figures? • • • • • • • 20.005 5.0900 5 000 3.006 7.0809 0.0350 31.670 • 0.0400 4 • 123.45 0 • 103.05 • 60.00 • 200.0 • 0.0070 0
  8. 8. How many significant figures are in the following measurements? 1. 30.0 2. 239 3. 0.890 4. 43.20 5. 1000 6. 34.42 7. 90.0 8. 0.0021 9. 5.400 10.0.0023 11.14.60 12.2 050 13.200.60 14.35 15.136.04 16.980.00 0 17.3. 18.570.0 19.0.700 20.12.040 21.460.13 22.15.010 23.19.80 24.0.0400 1
  9. 9. Adding and Subtracting  The result must be rounded off to have the same number of decimal places as the quantity with the least number of decimal places. Examples:  0.0836 + 195.2 = 195.3 10.00  2.67 + 7.3333 =  3.5212 – 3.12 = 0.40  6 – 0.384 =6
  10. 10. Multiplying and Dividing  The result must be rounded off to have Examples: 6.53 0.0390 the same number  0.0620 × 105.30 = of significant 500  3.000 × 0.0130 = figures as the  1000. / 2.010 = quantity with the  9 / 0.765 = least number of significant figures.
  11. 11. Practice Work. 1. 2. 3. 4. 5. 6. 7. 8. 37.76 + 3.907 + 226.4 = ? 319.15 - 32.614 = ? 104.630 + 27.08362 + 0.61 = ? 125 - 0.23 + 4.109 = ? 2.02 × 2.5 = ? 600.0 / 5.2302 = ? 0.0032 × 273 = ? 3 (5.5) = ?
  12. 12. Practice Work. 1. 37.76 + 3.907 + 226.4 = 268.1 2. 319.15 - 32.614 = 286.54 3. 104.630 + 27.08362 + 0.61 = 132.32 4. 125 - 0.23 + 4.109 = 128.879 ~ 129 5. 2.02 × 2.5 = 5.05 ~ 5.1 6. 600.0 / 5.2302 = 114.7183364 ~ 114.7 7. 0.0032 × 273 = 0.8736 ~ 0.87 3 8. (5.5) = 166.375 ~ 170
  13. 13. Practice Work. 9. 0.556 × (40 - 32.5) = ? 10. 45 × 3.00 = ? 11. What is the average of 0.1707, 0.1713, 0.1720, 0.1704, and 0.1715? 5 2 12. 3.00 x 10 - 1.5 x 10 = ? (Give the exact numerical result, and then express that result to the correct number of significant figures).

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