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Understanding Significant Figures in Scientific Notation

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Learn about scientific notation, significant figures, and their application in calculations involving atoms, measurements, and operations. Enhance your precision and accuracy skills in science.

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Understanding Significant Figures in Scientific Notation

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  1. Significant Figures Unit 1 Presentation 3

  2. The number of atoms in 12 g of carbon: 602,200,000,000,000,000,000,000 The mass of a single carbon atom in grams: 0.0000000000000000000000199 Scientific Notation 6.022 x 1023 1.99 x 10-23 N x 10n N is a number between 1 and 10 n is a positive or negative integer

  3. move decimal left move decimal right Scientific Notation 568.762 0.00000772 n > 0 n < 0 568.762 = 5.68762 x 102 0.00000772 = 7.72 x 10-6 Addition or Subtraction • Write each quantity with the same exponent n • Combine N1 and N2 • The exponent, n, remains the same 4.31 x 104 + 3.9 x 103 =

  4. Scientific Notation Multiplication (4.0 x 10-5) x (7.0 x 103) = • Multiply N1 and N2 • Add exponents n1and n2 Division 8.5 x 104÷ 5.0 x 109 = • Divide N1 and N2 • Subtract exponents n1and n2

  5. 1 2 3 4 5 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.

  6. Significant figures (sig figs) • The more marks the better we can estimate. • Scientists understand that the last number measured is actually an estimate 1 2 3 4 5

  7. 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

  8. 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

  9. 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.

  10. 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

  11. 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

  12. 27.93 + 6.4 27.93 27.93 + 6.4 6.4 For example • First line up the decimal places Then do the adding Find the estimated numbers in the problem 34.33 This answer must be rounded to the tenths place

  13. Practice • 4.8 + 6.8765 • 520 + 94.98 • 0.0045 + 2.113 • 6.0 x 102 - 3.8 x 103 • 5.4 - 3.28 • 6.7 - .542 • 500 -126 • 6.0 x 10-2 - 3.8 x 10-3

  14. 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!

  15. 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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