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Significant Figures

Significant Figures. What is a significant Figure?. Sig figs consist of all the digits known with certainty plus one final digit, which is somewhat uncertain or is estimated.

charlene-durham
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Significant Figures

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  1. Significant Figures

  2. What is a significant Figure? • Sig figs consist of all the digits known with certainty plus one final digit, which is somewhat uncertain or is estimated. • Say a nail is between 6.3cm and 6.4cm. And a final answer of around 6.36 cm. All digits including the uncertain one are significant. • Significant does not mean certain.

  3. How to determine the number • Process is easy if there are no zeros. It is just how many numbers there are. • Ex: • 13.2 has 3 sig figs • 9857 has 4 sig figs • 3 has 1 sig figs

  4. What if the number has a zero??

  5. There are rules!! • Zeros appearing between nonzero digits are significant. Ex. 40.7 has 3 sig figs. 87009 has 5 sig figs. • Zeros appearing in front of all nonzero digits are not significant. Ex. 0.095897 has 5 sig figs. .00009 has 1 sig fig. • Zeros at the end of a number to the right of a decimal point are significant. Ex. 85.00 has 4 sig figs. 9.000000000 has 10 sig figs.

  6. Rules continued… • Zeros at the end of a number but to the left of a decimal point may or may not be significant. If a zero has not been measured or estimated but is just a placeholder, it is not significant. A decimal point placed after zeros indicates that they are significant. • Ex. 2000 may contain from 1 to 4 sig figs, depending on how many zeros are placeholders. For measures in text assume that 2000 has 1 sig fig. 2000. contains 4 sig figs indicated by the presence of the decimal point.

  7. How many sig figs are in each of the following measurements? • 28.6 g • 3440. cm • 910 m • .04604 L • .0067000 kg

  8. Your turn! • 804.05 g • 0.0144030 km • 1002 m • 400 mL • 30000. cm • .00062500 kg

  9. Adding and subtracting sig figs • 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. • Ex. 25.1 g + 2.03 g = 27.13 g = 27.1 g • When using whole numbers, the answer should be rounded so that the final sig digit is in the same place as the left most uncertain digit. • Ex. 5400 + 365 = 5765 = 5800

  10. Add or subtract. Use the correct number of sig figs • 150.0 + .507 = • 7.56 + .375 + 14.0223 = • 98 – 50 = • 80. – 16 = • 76.90 + 1007.1 =

  11. Multiply and divide sig figs • The answer can have no more sig figs than are in the measurement with the fewest number of sig figs. • Ex. 3.05 g ÷ 8.47 mL = 0.36009 g/mL = 0.360 • Ex. 2.4 g/mL X 15.82 mL = 37.968 = 38 g

  12. Multiply or divide use the correct number of sig figs • 10.1 X 12.07 = • 70 x 2.4 = • 3.98 ÷ 2.3 = • 12.4 X 34 = • 320. ÷ 0.076 =

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