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## Scientific Notation

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**Scientific Notation**• A convenient way to express very large or very small numbers N x 10n Coefficient Must be 1≤N<10 Exponent (+)—large number (-)—small number**Taking #’s out of Sci. Notation**For POSITIVE exponents, move the decimal to the RIGHT…positive exponents make LARGE amounts. For NEGATIVE exponents, move the decimal to the LEFT…negative exponents make SMALL amounts. 9.998 x 109 5.007 x 104 3.45 x 10-2 6.76 x 10-6**Putting #s into Sci. Notation**Move the decimal until it is positioned between the first and second NON ZERO digits. Remember that positive exponents make LARGE amounts and negative exponents make SMALL amounts. 0.0000504 41,000,000 50 0.01201**Practice**• 1-20**Multiplying with Sci. Notation**• Multiply the coefficients • Add the exponents • Adjust the answer so that the coefficient is 1≤N<10 (4.0 x 102)(2.0 x 10-12)**Dividing with Sci. Notation**• Divide the coefficients. • Subtract the exponents. • Adjust the answer so that the coefficient is 1 ≤ N<10. 5.0 x 107 2.0 x 103**2.0 x 1012**4.0 x 10-3**Practice**• 21-28**Notes sheet #1 and 2**• All available digits + 1 estimated digit • A. 87.5oC B. 13.0 mL C. 4.15 cm The estimated digit is given in red.**Accuracy**• the agreement between experimental data and a known value. Example: Which one is more accurate?**Precision**• how well experimental values agree with each other Example: Which data is most precise? Is it accurate?**Draw a target diagram that shows both accuracy and precision****#7**Each of five students used the same ruler to measure the length of the same pencil. These data resulted: 15.33 cm, 15.34 cm, 15.33 cm, 15.33 cm, and 15.34 cm. The actual length of the pencil was 15.85 cm. Describe whether accuracy and precision are each good or poor for these measurements.**A measurement was taken three times. The correct measurement**was 68.1 mL. Circle whether the set of measurements is accurate, precise, both, or neither. • 78.1 mL, 43.9 mL, 2 mL accurate precise both neither • 68.1 mL, 68.2 mL, 68.0 mL accurate precise both neither • 98.0 mL, 98.2 mL, 97.9 mL accurate precise both neither • 72.0 mL, 60.3 mL, 68.1 mL accurate precise both neither**Decimal--Left**• If a number has a decimal, count all digits starting with the first non-zero digit on the left. • Examples: 0.004703 has 4 significant digits. 18.00 also has 4 significant digits.**No decimal--right**• If there is no decimal ,count all digits starting with the first non-zero digit on the right. • Examples: 140,000 has 2 significant digits. 20060 has 4 significant digits.**In both cases, start counting with the first non-zero digit.**00.015 15000**Now Try it on your paper**a) 3.57 m _________ b) 20.040 g _________ c) 0.004 m3_________ d) 730 000 kg _________ e) 12 700. mL _________ f) 30 atoms _________ g) 0.6034 g/mL _________ h) 19.0 s _________ i) 810 oC _________ j) 0.0100 mol_________ k) 0.0040 km _________ l) 8100.0 cm3_________ Complete Sig Fig Self Test**Math with sig figs**• Calculations shouldn't have more precision than the least precise measurement. • This leads to 2 rules: add/subtract & multiply/divide**Addition and Subtraction**• The answer should not have more decimal places than the number with the least decimal places. • Example: 1.2 + 12.348 = 4.2 + 8.579 =**Addition Practice**A) 345.6 + 456.78 = B) 4.42 + 8.576 = C) 23.456 + 0.04 = D) 78.2 - 40 = E) 87.9 – 20 = F) 478.84 – 119 =**Assignment**Top half of practice sheet (Addition and Subtraction sets only)**2. For Multiplication and Division**• The answer should not have more significant figures than the number with the least amount of significant figures. • Example: 502 x 3.6 = 1807.2 1800**Multiplication Practice**A) 238.1 x 402 = B) 500.1 x 75.2 = C) 23.02 / 45 = D) 5300 / 456 = E) 4590 / 1234 = F) 141 x 920.0 =