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Chapter 1 Section 3: Measurements and Calculations in Chemistry

Objectives: (1)To determine the number of significant figures in a measurement. (2) To perform calculations using significant figures. Chapter 1 Section 3: Measurements and Calculations in Chemistry. Accuracy and Precision.

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Chapter 1 Section 3: Measurements and Calculations in Chemistry

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  1. Objectives: (1)To determine the number of significant figures in a measurement.(2) To perform calculations using significant figures.

  2. Chapter 1Section 3: Measurements and Calculations in Chemistry

  3. Accuracy and Precision • Accuracy is a description of how close a measurement is to the true value of the quantity measured. • Precision is the exactness of a measurement.

  4. Accuracy and Precision BOTH PRECISE AND ACCURATE NEITHER PRECISE NOR ACCURATE PRECISE BUT NOT ACCURATE

  5. Significant Figures (sig figs) • Sig Figs tell us how good the data we are using are.

  6. Rules for Determining Sig Figs • All non-zero digits are significant. 123 = 3 sig figs 8,476 = 4 sig figs 934,526 = 6 sig figs

  7. 2. All zeros, between non-zero digits, are significant. 101 = 3 sig figs 2,000,503 = 7 sig figs 3,009 = 4 sig figs

  8. 3. Reading left to right, all ending zeros, without a decimal point, are not significant. 6,000 = 1 sig fig 120 = 2 sig figs 407,000 = 3 sig figs

  9. 4. Reading left to right, all ending zeros, with a decimal point, are significant. 400. = 3 sig figs 122.000 = 6 sig figs 5,020.0 = 5 sig figs

  10. 5. Reading left to right, all starting zeros after a decimal point are not significant. 0.0012 = 2 sig figs 0.0609 = 3 sig figs 0.000000003 = 1 sig fig

  11. How Many Sig Figs? • 25 cm • 305 cm • 0.00123 in • 400 g • 400. m • 0.94600 mL

  12. How Many Sig Figs? • 25 cm = 2 • 305 cm = 3 • 0.00123 in = 3 • 400 g = 1 • 400. m = 3 • 0.94600 mL = 5

  13. Answers a.) 5,490,000 m b.) 0.0134793 mL c.) 31,950 cm2 d.) 192.67 m2 e.) 790 cm f.) 389,278,000 J

  14. Calculations with Sig Figs:Addition and Subtraction Your answer can only be as accurate as the least accurate measurement used in the calculation. • Complete the calculation. • Determine the number of digits to the right of the decimal point in each measurement used in the calculations. • Round answer so that it has that same number of digits to the right of the decimal as the measurement with the smallest number of digits to the right of the decimal. Example: 3.95 g + 2.87 g + 213.6 g

  15. Example 3.95 g + 2.87 g + 213.6 g = 220.42 g 3.95 g has 2 numbers after the decimal 2.87 g has 2 numbers after the decimal point 213.6 g has 1 number after the decimal point Therefore, the answer must have 1 number after the decimal point. Answer = 220.4 g

  16. Example Solve: 4.999 mL – 1.2 mL 4.999 mL – 1.2 mL = 3.799 mL 4.999 mL has 3 numbers after the decimal 1.2 mL has 1 number after the decimal Therefore, the answer must have 1 number after the decimal. Answer = 3.8 mL

  17. Practice 1.) 0.1273 mL – 0.008 mL 2.) 1.222 cm + 3.55 cm + 1.0 cm 3.) 3.2 g – 1.4 g + 0.33 g 4.) 34.09 L – 1.230 L 5.) 32.89 g + 14.21 g

  18. AnswersDON’T FORGET UNITS! 1.) 0.1273 mL – 0.008 mL = 0.1193 mL  0.119 mL 2.) 1.222 cm + 3.55 cm + 1.0 cm = 5.772 cm  5.8 cm 3.) 3.2 g – 1.4 g + 0.33 g = 2.13 g  2.1 g 4.) 34.09 L – 1.230 L = 32.860 L  32.86 L 5.) 32.89 g + 14.21 g = 47.1 g  47.10 g

  19. Calculations with Sig FigsMultiplication and Division Your answer can only be as accurate as the least accurate measurement used in the calculation. • Complete the calculation. • Determine the number of sig figs in each measurement used in the calculations. • Round answer to the same number of sig figs as the least accurate measurement. Example: 651 cm x 75 cm

  20. Example Solve: 651 cm x 75 cm 651 cm x 75 cm = 48825 cm2 651 cm has 3 sig figs 75 cm has 2 sig figs Therefore, the answer must have 2 sig figs. Answer = 49000 cm2

  21. Practice Perform the following calculations and express the answer in the correct units and number of sig figs. 1.) 7.835 kg / 2.5 L 2.) 14.75 L / 1.20 s 3.) 360 cm x 51 cm x 9.07 cm 4.) 5.18 m x 0.77 m x 10.22 m 5.) 34.95 g / 11.169 cm3

  22. Answers Perform the following calculations and express the answer in the correct units and number of sig figs. 1.) 7.835 kg / 2.5 L = 3.1 kg/L 2.) 14.75 L / 1.20 s = 12.34 s 3.) 360 cm x 51 cm x 9.07 cm = 170,000 cm3 4.) 5.18 m x 0.77 m x 10.22 m = 41 m3 5.) 34.95 g / 11.169 cm3 = 3.129 g/cm3

  23. Practice 1.) (12.4 cm x 7.943 cm) + 0.0064 cm2 2.) (246.83 g/26) – 1.349 g

  24. Answer 1.) (12.4 cm x 7.943 cm) + 0.0064 cm2 First multiply and second add. 12.4 cm x 7.943 cm = 98.4932  98.5 cm2 98.5 cm2 + 0.0064 cm2 = 98.50064 cm2  98.5 cm2 2.) (246.83 g/26) – 1.349 g First divide and second subtract. 246.83 g/26 = 9.4934615 g  9.5 g 9.5 g – 1.349 g = 8.151 g  8.2 g

  25. A rectangle measures 87.59 cm by 35.1 mm. Express its area with the proper number of sig figs in the specified unit: in cm2 in mm2 in m2

  26. Answer A rectangle measures 87.59 cm by 35.1 mm. Express its area with the proper number of sig figs in the specified unit: in cm2 : 87.59 cm x 3.51 cm = 307 cm2 in mm2 : 875.8 mm x 35.1 mm = 30700 mm2 in m2 : 0.8759 m x 0.0351 m = 0.0307 m2

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