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Scientific Notation

Learn about converting, calculating, and counting with scientific notation, significant figures, accuracy vs. precision, and percent error. Understand how to use exact numbers and solve practice problems. Improve your chemistry math skills now.

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Scientific Notation

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  1. Scientific Notation • Converting into Sci. Notation: • Move decimal until there’s 1 digit to its left. Places moved = exponent. • Large # (>1)  positive exponentSmall # (<1)  negative exponent • Only include sig figs. 65,000 kg  6.5 × 104 kg

  2. 1. 2,400,000 g 2. 0.00256 kg 3. 7  10-5 km 4. 6.2  104 mm Scientific Notation Practice Problems 2.4  106 g 2.56  10-3 kg 0.00007 km 62,000 mm

  3. EXE EXP EXP ENTER EE EE Calculating with Scientific Notation Example: (5.44 × 107 g) ÷ (8.1 × 104 mol) = Type on your calculator: 5.44 7 8.1 4 ÷ = 671.6049383 = 670 g/mol = 6.7 × 102 g/mol

  4. Chemistry Math Accuracy and Precision Percent Error Significant Figures

  5. A. Accuracy vs. Precision • Accuracy – a measure of how close a measurement comes to the true value • Precision – a measure of how close a series of measurements are to one another. ACCURATE = CORRECT PRECISE = CONSISTENT

  6. Example: Low accuracy – high precision High accuracy – low precision High accuracy – high precision

  7. your value true value B. Calculating Percent Error • Error – the difference between the experimental value and the accepted value.

  8. B. Percent Error • A student determines the density of a substance to be 1.40 g/mL. Find the error and the % error if the accepted value of the density is 1.36 g/mL.

  9. SIGNIFICANT FIGURES 8 9 A New Way To Count Numbers 2 4 3 7 0 5

  10. C. Significant Figures • Indicates the precision of a measurement. • Recording Sig Figs • Sig figs in a measurement include the known digits plus a final estimated digit 2.35 cm

  11. 2.83 cm 4.50 cm 15.0 oC 28.5 oC 30.0 mL 4.29 mL

  12. C. Significant Figures • Counting Sig Figs • Count all numbers EXCEPT: • Leading zeros -- 0.0025 • Trailing zeros without a decimal point -- 2,500

  13. C. Significant Figures Counting Sig Fig Examples 1. 23.50 1.23.50 4 sig figs 3 sig figs 2. 402 2.402 3. 5,280 3.5,280 3 sig figs 2 sig figs 4. 0.080 4. 0.080

  14. C. Significant Figures • Calculating with Sig Figs • Add/Subtract - The # with the lowest decimal value determines the place of the last sig fig in the answer. 3.75 mL + 4.1 mL 7.85 mL 3.75 mL + 4.1 mL 7.85 mL 224 g + 130 g 354 g 224 g + 130 g 354 g  350 g  7.9 mL

  15. 3 SF C. Significant Figures • Calculating with Sig Figs • Multiply/Divide - The # with the fewest sig figs determines the # of sig figs in the answer. (13.91g/cm3)(23.3cm3) = 324.103g 4 SF 3 SF 324g

  16. EXACT NUMBERS • Exact numbers have infinite number of significant figures. Exact numbers include • Counting of anything : 22 people or 10 meter sticks, 6 eggs etc. • Defined quantities : 12 = 1 doz. • Exact numbers do not affect the rounding to the correct number of significant figures or in the calculations of the measurements.

  17. 1. (15.30 g) ÷ (6.4 mL)  2.4 g/mL 2 SF C. Significant Figures Practice Problems 4 SF 2 SF = 2.390625 g/mL 2. 18.9 g - 0.84 g  18.1 g 18.06 g

  18. Practice Problems (pg. 70 &71). • 3). 61.2 meters + 9.35 meters + 8.6 meters = • 4). 8.3 meters x 2.22 meters= • 5). 8.345 g / 10.6 mL =

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