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Scientific Notation

Scientific Notation. Converting into Sci. Notation: Move decimal until there’s 1 digit to its left. Places moved = exponent. Large # (>1)  positive exponent Small # (<1)  negative exponent Only include sig figs. 65,000 kg  6.5 × 10 4 kg. 1. 2,400,000 g 2. 0.00256 kg

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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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