Significant Figures and Scientific Notations

1. Significant Figures and Scientific Notations Examples and Problems

2. Rules for Counting Significant Figures 1. Nonzero integers always count as significant figures. 2. Zeros: There are three classes of zeroes. • Leading zeroes precede all the nonzero digits and DO NOT count as • significant figures. Example: 0.0025 has ____ significant figures. • Captive zeroes are zeroes between nonzero numbers. These always • count as significant figures. Example: 1.008 has ____ significant figures. • 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 102 has ____ significant figures. • Trailing zeroes are not significant if the number does not contain a decimal • point. Example: 100 has ____ significant figure. • 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. 2 4 3 1 Ohn-Sabatello, Morlan, Knoespel, Fast Track to a 5 Preparing for the AP Chemistry Examination2006, page 53

3. Significant figures: Rules for zeros Leading zeros are not significant. Leading zero – three significant figures 0.421 Captive zeros are significant. Captive zero 4012 – four significant figures Trailing zeros are significant. Trailing zero 114.20 – five significant figures

4. Significant Figures • Counting Sig Figs • Count all numbers EXCEPT: • Leading zeros -- 0.0025 • Trailing zeros without a decimal point -- 2,500 Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

5. 3 SF Significant Figures • Calculating with Sig Figs • Multiply/Divide - The # with the fewest sig figs determines the # of sig figs in the answer. (13.91g/cm3)(23.3cm3) = 324.103g 4 SF 3 SF 324g Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

6. 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. 224 g + 130 g 354 g 224 g + 130 g 354 g 3.75 mL + 4.1 mL 7.85 mL 3.75 mL + 4.1 mL 7.85 mL  350 g  7.9 mL Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

7. 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 www.nisd.net/communicationsarts/pages/chem

8. 1. (15.30 g) ÷ (6.4 mL)  2.4 g/mL 2 SF Significant Figures Practice Problems 4 SF 2 SF = 2.390625 g/mL 2. 18.9 g - 0.84 g  18.1 g 18.06 g Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

9. Scientific Notation 65,000 kg  6.5 × 104 kg • Converting into scientific notation: • Move decimal until there’s 1 digit to its left. Places moved = exponent. • Large # (>1)  positive exponentSmall # (<1)  negative exponent • Only include sig. figs. Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

10. 3. 2,400,000 g 4. 0.00256 kg 5. 7  10-5 km 6. 6.2  104 mm Scientific Notation Practice Problems 2.4  106 g 2.56  10-3 kg 0.00007 km 62,000 mm Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

11. EXE EXP EXP ENTER EE EE Scientific Notation • Calculating with scientific notation (5.44 × 107 g) ÷ (8.1 × 104 mol) = Type on your calculator: 5.44 7 8.1 4 ÷ = 671.6049383 = 670 g/mol = 6.7 × 102 g/mol Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem