CH. 2 - MEASUREMENT I. Using Measurements

A. Accuracy vs. Precision Accuracy - how close a measurement is to the accepted value Precision - how close a series of measurements are to each other ACCURATE = CORRECT PRECISE = CONSISTENT

B. Percent Error Indicates accuracy of a measurement your value accepted value

B. Percent Error % error = 2.9 % A student determines the density of a substance to be 1.40 g/mL. Find the % error if the accepted value of the density is 1.36 g/mL. % error = 2.9 %

C. 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

C. Significant Figures Counting Sig Figs (Table 2-5, p.47) Count all numbers EXCEPT: Leading zeros -- 0.0025 Trailing zeros without a decimal point -- 2,500

Counting Sig Fig Examples C. Significant Figures Counting Sig Fig Examples 1. 23.50 1. 23.50 4 sig figs 2. 402 2. 402 3 sig figs 3. 5,280 3. 5,280 3 sig figs 4. 0.080 4. 0.080 2 sig figs

C. Significant Figures (13.91g/cm3)(23.3cm3) = 324.103g 324 g 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 3 SF 324 g

C. Significant Figures 3.75 mL + 4.1 mL 7.85 mL 3.75 mL + 4.1 mL 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. 3.75 mL + 4.1 mL 7.85 mL 3.75 mL + 4.1 mL 7.85 mL 224 g + 130 g 354 g 224 g + 130 g 354 g  7.9 mL  350 g

C. 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

C. Significant Figures Practice Problems 5. (15.30 g) ÷ (6.4 mL) 4 SF 2 SF = 2.390625 g/mL  2.4 g/mL 2 SF 6. 18.9 g - 0.84 g  18.1 g 18.06 g

D. Scientific Notation 65,000 kg  6.5 × 104 kg Converting into Sci. 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.

D. Scientific Notation Practice Problems 7. 2,400,000 g 8. 0.00256 kg 9. 7  10-5 km 10. 6.2  104 mm 2.4  106 g 2.56  10-3 kg 0.00007 km 62,000 mm

D. Scientific Notation Calculating with Sci. Notation (5.44 × 107 g) ÷ (8.1 × 104 mol) = Type on your calculator: EXP EE EXP EE ENTER EXE 5.44 7 8.1 ÷ 4 = 671.6049383 = 670 g/mol = 6.7 × 102 g/mol

E. Proportions Direct Proportion y x Inverse Proportion y x