Significant Figures and Scientific Notations Examples and Problems

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

Significant figures: Rules for zeros Leading zeros are not significant. Captive zeros are significant. Trailing zeros are significant. Leading zero Captive zero Trailing zero – three significant figures – four significant figures – five significant figures

Significant Figures Counting Sig Figs –Count all numbers EXCEPT: Leading zeros Trailing zeros without a decimal point -- 2,500 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 1. (15.30 g) ÷ (6.4 mL) Practice Problems = g/mL  18.1 g g 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 3. 2,400,000  g kg 5. 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