06 significant figures
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Significant figures are used to indicate the precision of measurement in a calculation or measurement. There are three main rules for determining which figures in a number are significant: 1) non-zero digits are always significant, 2) zeros between significant figures are significant, and 3) trailing zeros are only significant if a decimal is present. The number of significant figures impacts how numbers are rounded in calculations, with addition/subtraction rounding to the least decimal places and multiplication/division rounding to the least significant figures. Practice problems are provided to demonstrate applications of significant figures in calculations and measurements.
06 significant figures
- 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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).