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Significant Figures

Understand the rules for significant figures usage in scientific measurements and enhance accuracy in reporting data.

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Significant Figures

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  1. Chapter 2 Section 3 Using Scientific Measurements Significant Figures • Significant figures in a measurement consist of all the digits known with certainty plus one final digit, which is somewhat uncertain or is estimated. • Significant figures are critical when reporting scientific data because they give the reader an idea of how well you could actually measure/report your data. • We don’t worry about significant figures when using “exact” numbers, because they are known with complete certainty.

  2. Reporting Measurements Using Significant Figures

  3. Rules for deciding the number of significant figures in a measured quantity: • (1) All nonzero digits are significant: • 1.234 g has 4 significant figures • (2) Zeroes between nonzero digits are significant: • 1002 kg has 4 significant figures • (3) Leading zeros to the left of the first nonzero digits are not significant; such zeroes merely indicate the position of the decimal point: • 0.001 oC has only 1 significant figure • (4) Trailing zeroes that are also to the right of a decimal point in a number are significant: • 0.0230 mL has 3 significant figures

  4. (5) When a number ends in zeroes that are not to the right of a decimal point, the zeroes are not necessarily significant: 190 miles may be 2 or 3 significant figures,50,600 calories may be 3, 4, or 5 significant figures. The potential ambiguity in the last rule can be avoided by the use of standard exponential, or "scientific," notation. For example, depending on whether the number of significant figures is 3, 4, or 5, we would write 50,600 calories as: 5.06 × 104 calories (3 significant figures)5.060 × 104 calories (4 significant figures), or5.0600 × 104 calories (5 significant figures). By writing a number in scientific notation, the number of significant figures is clearly indicated by the number of numerical figures in the 'digit' term as shown by these examples.

  5. Significant Figures • How many significant figures are in each of the following measurements? • a. 28.6 g • b. 3440. cm • c. 910 m • d. 0.046 04 L • e. 0.006 700 0 kg • f. 3.05 x 104 g • g. 60.004 mg

  6. Lets try some more. How many significant figures are there in the following measurements: • 45.0 cm ______ • 1200.0 km ______ • .0045 m ______ • 1.020 g ______ • 6500. m ______ • 4.00 L ______ • .0025 km ______ • 67.003 g ______

  7. Significant Figures Addition or Subtraction with Significant Figures • When adding or subtracting decimals, the answer must have the same number of digits to the right of the decimal point as there are in the measurement having the fewest digits to the right of the decimal point. Multiplication or Division with Significant Figures • For multiplication or division, the answer can have no more significant figures than are in the measurement with the fewest number of significant figures.

  8. Significant Figures • Sample Problem • Carry out the following calculations. Expresseach answer to the correct number of significantfigures. • a. 5.44 m + 2.6103 m • b. 2.4 g/mL  15.82 mL

  9. Let’s try a couple practice problems. • 4503 + 34.90 + 550 = ? • 1.367 - 1.34 = ? • 4.56 x 2.5 = ?

  10. Rounding Off Numbers In correcting a number to express the proper number of sig. fig., we often have to drop off unwanted digits. Rules for rounding off numbers: If the digit immediately to the right of the last sig. fig. is more than 5, you round up. If the digit immediately to the right of the last sig. fig. is less than 5, you round down. 35.76 in 3 sig. fig. is 35.8 35.74 in 3 sig. fig. is 35.7

  11. If the digit immediately to the right of the last sig. fig. is equal to 5, you round up if the last sig. fig. is odd. You round down if the last sig. fig. is even. You round up if 5 is followed by nonzero digits, regardless of whether the last sig. fig. is odd or even. 24.35 in 3 sig. fig. is 24.4 (round up because last sig. digit is 3, an odd number) 24.25 in 3 sig. fig. is 24.2 (round down because last sig. digit is 2, an even number) 24.258 in 3 sig. fig. is 24.3 (round up because the digits 58 means it is past halfway to 24.3)

  12. Math using sig figs Practice Problems

  13. Addition/Subtraction • 34.702 cm 190.450 m • + 12.3 cm - 100.5 m • 45.0325 g 5.600 km • + 12.34 g - 2.30 km

  14. Multiplication/Division • 34.5 m x 1.2 m = • 1,200 kg x 2.3 kg = • 34.6 m / 4.2 = • .3400 g / 8.2

  15. Rounding • 43.48 cm (to 3 sig figs) = • 12.42 cm (to 3 sig figs) = • 9.275 g (to 3 sig figs) = • 20.35 g (to 3 sig figs) =

  16. Try these problems: 72.49 in 3 sig. fig. is ___________ 292000 in 2 sig. fig. is ___________ 45.52 in 3 sig. fig. is ___________ 92,528 in 4 sig. fig. is ___________ 120.05 in 4 sig. fig. is ___________ 13,052 in 3 sig. fig. is ___________ 239.5 in 3 sig. fig. is ___________ 2.448 x 104 in 3 sig. fig. is ___________ 28.149 in 3 sig. fig. is ___________ 32000.000 in 3 sig. fig. is ___________ 63500 in 2 sig. fig. is ___________ 89999 in 3 sig. fig. is ___________

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