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Calculations with Significant Figures

Calculations with Significant Figures. Sig Figs meet Rounding!. Background. In Science we take measurements, but those measurements are sometimes needed to find the values that we really want. For example: Volume (Length x Width x Height)

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Calculations with Significant Figures

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  1. Calculations with Significant Figures Sig Figs meet Rounding!

  2. Background • In Science we take measurements, but those measurements are sometimes needed to find the values that we really want. • For example: • Volume (Length x Width x Height) • Volume by Difference using a graduated cylinder (Height of Water with object – Height of water initially) • Density (Mass ÷ Volume) • Calculations cannot be more precise than the measurements.

  3. Adding and Subtracting Measurements • The least precise measurement dictates the precision of the answer • The least precise will be the measurement with the LEAST decimal places. • When adding or subtracting – pretend that you are back in elementary school and line those numbers up!

  4. Adding and Subtracting Measurements • Example: Two different pieces of metal are massed separately using different balances. The first piece has a mass of 19.473 g. The second piece has a mass of 3.82 g. What is the total mass? Don’t forget to use significant figures. • Step 1 – Line them up and do the math. 19.473 + 3.82 23.293

  5. Adding and Subtracting Measurements • Step 2 – Find the LAST significant figure. Start from the right. Look for the first column that has a significant figure from both measurements. Underline the number in the answer that is in that column. 19.473 + 3.82 23.293

  6. Adding and Subtracting Measurements • Step 3 – Round to that place – do not forget to LOOK right! 19.473 + 3.82 23.293 Answer : 23.29 g – Don’t forget the Unit!!!

  7. Adding and Subtracting Measurements • Subtraction is the SAME!!! • Example – The mass of a paper cup is 1.284 g. The mass of the paper cup plus a sample of Manmium is 38.2 g. What is the mass of the Manmium sample? Step 1 – What is it? 38.2 - 1.284 36.916 Yep – Line them up!

  8. Adding and Subtracting Measurements Step 2 – What is it? Yep – Underline the last significant figure! 38.2 - 1.284 36.916

  9. Adding and Subtracting Measurements Step 3 – What is it? Yep – Look right and ROUND! 38.2 - 1.284 36.916 Answer = 36.9 g

  10. Adding and Subtracting Practice • 489.2 g + 8.03 g = ? • 0.2800 L + 4.8 L =? • 285.0 kg – 3.82 kg = ? • 0.01963 g + 0.290 g =? • 926.028 kg – 30.02 kg = ? • 3902 L + 284.5 L = ?

  11. Adding and Subtracting Practice • 489.2 g + 8.03 g = 497.2 g • 0.2800 L + 4.8 L = 5.1 L • 285.0 kg – 3.82 kg = 281.2 kg • 0.01963 g + 0.290 g = 0.310 g • 926.028 kg – 30.02 kg = 896.01 kg • 3,902 L + 284.5 L = 4,186 L

  12. Multiplication and Division of Measurements • The least precise measurement dictates the precision of the answer • The least precise will be the measurement with the LEAST number of significant figures. • The answer should be rounded to the least number of significant figures

  13. Multiplication and Division of Measurements • Example: Find the area of a rectangle with a length of 24.35 m and a width of 4.09 m. • Step 1 – Do the math! • Area = Length x width • 24.35 m x 4.09 m = 99.5915 m2 • Step 2 – Determine the number of significant figures in the original measurements • 24.35 m (4 sig figs) • 4.09 m (3 sig figs)

  14. Multiplication and Division of Measurements • Step 3 – Determine the least number of sig figs • 3 sig figs is less than 4 sig figs • Step 4 – round the answer to the least number of sig figs that you determined in Step 3 • 99.5915 m2 • Final Answer – 99.6 m2

  15. Multiplication and Division of Measurements • Division is the same! • Example – An object has a mass of 48.309 g and a volume of 9.28 mL. What is the density of this object? • What is Step 1? • Yep – do the math! • Density = mass/volume • Density = 48.309 ÷ 9.28 = 5.20571121 g/mL

  16. Multiplication and Division of Measurements • What is Step 2? • Yep – determine the number of significant figures in each of the original measurements • 48.309 g (5 sig figs) • 9.28 mL ( 3 sig figs) • What is Step 3? • Yep – determine the least number of sig figs in the original measurements • 3 sig figs

  17. Multiplication and Division of Measurements • What is Step 4? • Yep – Round to the least number of sig figs found in Step 3 • 5.20571121 g/mL round to three sig figs • Final Answer = 5.21 g/mL

  18. Multiplication and Division Practice • 40.38 cm x 3.2903 cm = ? • 0.00382 m x 0.08291 m = ? • 293.0 g ÷ 3.0023 cm3 = ? • 3.0193 x 104 kg ÷ 4.93 L = ? • 293.0 cm x 3.28 cm = ? • Challenge: 3.927 cm x 12.736 cm x 4.000 cm = ?

  19. Multiplication and Division Practice • 40.38 cm x 3.2903 cm = 132.9 cm2 • 0.00382 m x 0.08291 m = 0.000317 m2or 3.17 x 10-4m2 • 293.0 g ÷ 3.0023 cm3 = 97.59 g/cm3 • 3.0193 x 104 kg ÷ 4.93 L = 6,120 kg/L or 6.12 x 103 kg/L • 293.0 cm x 3.28 cm = 89.3 cm2 • Challenge: 3.927 cm x 12.736 cm x 4.000 cm = 200.1 cm3

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