Significant Figures

Factor Name Symbol Factor Name Symbol decimeter dm 10 1 decameter dam centimeter cm 10 2 hectometer hm millimeter mm 10 3 kilometer km micrometer  m 10 6 megameter Mm nanometer nm 10 9 gigameter Gm picometer pm terameter Tm femtometer fm petameter Pm attometer am exameter Em zeptometer zm zettameter Zm yoctometer ym yottameter Ym

Scientific Notation: Powers of Ten Rules for writing numbers in scientific notation: Write all significant figures but only the significant figures. Place the decimal point after the first digit, making the number have a value between 1 and 10. Use the correct power of ten to place the decimal point properly, as indicated below. a) Positive exponents push the decimal point to the right. The number becomes larger. It is multiplied by the power of 10. b) Negative exponents push the decimal point to the left. The number becomes smaller. It is divided by the power of 10. c) 10 o = 1 Examples: 3400 = 3.40 x = 1.20 x 10-2 Nice visual display of Powers of Ten (a view from outer space to the inside of an atom) viewed by powers of 10!a view from outer space to the inside of an atom

Accuracy vs. Precision Random errors: reduce precision Good accuracy Good precision Poor accuracy Good precision Poor accuracy Poor precision Systematic errors: reduce accuracy (person)(instrument)

Precision Accuracy  reproducibility  check by repeating measurements  poor precision results from poor technique  correctness  check by using a different method  poor accuracy results from procedural or equipment flaws.

Reporting Measurements Using significant figures Report what is known with certainty Add ONE digit of uncertainty (estimation) Davis, Metcalfe, Williams, Castka, Modern Chemistry, 1999, page 46

Practice Measuring 4.5 cm 4.54 cm 3.0 cm Timberlake, Chemistry 7 th Edition, page 7 cm

Implied Range of Uncertainty Implied range of uncertainty in a measurement reported as 5 cm Implied range of uncertainty in a measurement reported as 5.0 cm. Dorin, Demmin, Gabel, Chemistry The Study of Matter 3rd Edition, page Implied range of uncertainty in a measurement reported as 5.00 cm.

20 10 ? 15 mL ? 15.0 mL1.50 x 10 1 mL

Significant Figures  Indicate precision of a measurement.  Recording Sig Figs  Sig figs in a measurement include the known digits plus a final estimated digit 2.35 cm Courtesy Christy Johannesson

Significant Figures  Counting Sig Figs  Count all numbers EXCEPT:  Leading zeros  Trailing zeros without a decimal point -- 2,500 Courtesy Christy Johannesson

, Significant Figures Counting Sig Fig Examples , sig figs 3 sig figs 2 sig figs Courtesy Christy Johannesson

Significant Figures  Calculating with Sig Figs  Multiply/Divide - The # with the fewest sig figs determines the # of sig figs in the answer. (13.91g/cm 3 )(23.3cm 3 ) = g 324 g 4 SF3 SF Courtesy Christy Johannesson

Significant Figures  Calculating with Sig Figs (con’t)  Add/Subtract - The # with the lowest decimal value determines the place of the last sig fig in the answer mL mL 7.85 mL 224 g g 354 g  7.9 mL  350 g 3.75 mL mL 7.85 mL 224 g g 354 g Courtesy Christy Johannesson

Significant Figures  Calculating with Sig Figs (con’t)  Exact Numbers do not limit the # of sig figs in the answer.  Counting numbers: 12 students  Exact conversions: 1 m = 100 cm  “1” in any conversion: 1 in = 2.54 cm Courtesy Christy Johannesson

Significant Figures (15.30 g) ÷ (6.4 mL) Practice Problems = g/mL  18.1 g 18.9g g g 4 SF2 SF  2.4 g/mL 2 SF Courtesy Christy Johannesson

Scientific Notation  Converting into scientific 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 Courtesy Christy Johannesson

Scientific Notation 7. 2,400,000  g kg 9.7  km  10 4 mm Practice Problems 2.4  10 6  g 2.56  kg km 62,000 mm Courtesy Christy Johannesson

Scientific Notation  Calculating with scientific notation (5.44 × 10 7 g) ÷ (8.1 × 10 4 mol) = 5.44 EXP EE ÷ ÷ EXP EE ENTER EXE = = 670 g/mol= 6.7 × 10 2 g/mol Type on your calculator: Courtesy Christy Johannesson

Proportions  Direct Proportion  Inverse Proportion y x y x Courtesy Christy Johannesson

Rules for Counting Significant Figures 1. Nonzero integers always count as significant figures. 2. Zeros: There are three classes of zeroes. a.Leading zeroes precede all the nonzero digits and DO NOT count as significant figures. Example: has ____ significant figures. b.Captive zeroes are zeroes between nonzero numbers. These always count as significant figures. Example: has ____ significant figures. c.Trailing zeroes are zeroes at the right end of the number. Trailing zeroes are only significant if the number contains a decimal point. Example: 1.00 x 10 2 has ____ significant figures. Trailing zeroes are not significant if the number does not contain a decimal point. Example: 100 has ____ significant figure. 3.Exact numbers, which can arise from counting or definitions such as 1 in = 2.54 cm, never limit the number of significant figures in a calculation Ohn-Sabatello, Morlan, Knoespel, Fast Track to a 5 Preparing for the AP Chemistry Examination 2006, page 53