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Significant Figures Unit 1 Presentation 3

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Scientific Notation The number of atoms in 12 g of carbon: 602,200,000,000,000,000,000,000 6.022 x 10 23 The mass of a single carbon atom in grams: 0.0000000000000000000000199 1.99 x 10 -23 N x 10 n N is a number between 1 and 10 n is a positive or negative integer

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Scientific Notation 568.762 n > 0 568.762 = 5.68762 x 10 2 move decimal left 0.00000772 n < 0 0.00000772 = 7.72 x 10 -6 move decimal right Addition or Subtraction 1.Write each quantity with the same exponent n 2.Combine N 1 and N 2 3.The exponent, n, remains the same 4.31 x 10 4 + 3.9 x 10 3 =

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Scientific Notation Multiplication 1.Multiply N 1 and N 2 2.Add exponents n 1 and n 2 (4.0 x 10 -5 ) x (7.0 x 10 3 ) = Division 1.Divide N 1 and N 2 2.Subtract exponents n 1 and n 2 8.5 x 10 4 ÷ 5.0 x 10 9 =

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Significant figures (sig figs) How many numbers in a measurement mean something When we measure something, we can (and do) always estimate between the smallest marks. 21345

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Significant figures (sig figs) The more marks the better we can estimate. Scientists understand that the last number measured is actually an estimate 21345

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Sig Figs What is the smallest mark on the ruler that measures 142.15 cm? 142 cm? 140 cm? Here there’s a problem: Does the zero count or not? Scientists needed a set of rules to decide which zeroes count. All other numbers always count

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Which zeros count? Leading zeros never count –0.045 Trapped zeros always count –100365405.057 Trailing zeros only count if there is a decimal place present –12400 Here the zeroes do NOT count –12400. Here the zeroes DO count

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Sig Figs Only measurements have sig figs. Counted numbers are always exact –A dozen is exactly 12 A a piece of paper is measured 11 inches tall. Being able to locate, and count significant figures is an important skill.

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Sig figs. Count the sig figs and the number of significant zeros in the following numbers –458 g –4085 g –4850 g –0.0485 g –0.004085 g –40.004085 g

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Adding and subtracting with significant figures The last significant figure in a measurement is an estimate. Your answer can not be better (more precise) than your worst (least-precise) estimate. You have to round it to the least place of precision of the measurement in the problem

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For example 27.936.4+ l First line up the decimal places 27.93 6.4+ Then do the adding 34.33 Find the estimated numbers in the problem 27.93 6.4 This answer must be rounded to the tenths place

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Practice 4.8 + 6.8765 520 + 94.98 0.0045 + 2.113 6.0 x 10 2 - 3.8 x 10 3 5.4 - 3.28 6.7 -.542 500 -126 6.0 x 10 -2 - 3.8 x 10 -3

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Multiplication and Division Rule is simpler Answer will have the same number of sig figs as the value with the least number of sig figs in the problem 3.6 x 653 = 2350.8 3.6 has 2 s.f. 653 has 3 s.f. answer can only have 2 s.f. 2400 Note that there is NO decimal point present!

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Multiplication and Division Same rules for division Lets do some practice. 4.5 / 6.245 4.5 x 6.245 9.8764 x.043 3.876 / 1983 16547 / 714

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