Using Measurements

1. Measurements and Calculations Using Measurements

2. 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

3. your value accepted value Percent Error • Indicates accuracy of a measurement

4. % error = 2.9 % Percent Error • 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.

5. 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

6. Significant Figures • Counting Sig Figs(Table 2-5, p.39) • Count all numbers EXCEPT: • Leading zeros -- 0.0025 • Trailing zeros without a decimal point -- 2,500

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

8. 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

9. C. 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

10. 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

11. (15.30 g) ÷ (6.4 mL)  2.4 g/mL 2 SF Significant Figures Practice Problems 4 SF 2 SF = 2.390625 g/mL 18.9 g - 0.84 g  18.1 g 18.06 g

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

13. 1. 2,400,000 g 2. 0.00256 kg 3. 7  10-5 km 4. 6.2  104 mm Scientific Notation Practice Problems 2.4  106 g 2.56  10-3 kg 0.00007 km 62,000 mm

14. Calculating with Scientific Notation • Addition and Subtraction • All numbers are converted to the same power of 10 • Digit terms are added or subtracted • Example: • (4.215 x 10-2 g) + (3.2 x 10-4 g) = • (4.215 x 10-2 g) + (0.032 x 10-2 g) = 4.247 x 10-2 g • = 4.247 x 10-2 g • Answer must be rounded correctly DON’T forget the UNITS

15. Calculating with Scientific Notation • Addition and Subtraction • All numbers are converted to the same power of 10 • Digit terms are added or subtracted • Example: • (8.97 x 104g) - (2.62 x 103 g) = • (8.97 x 104 g) - (0.262 x 104 g) = 8.708 x 104 g • = 8.71 x 104 g • Answer must be rounded correctly DON’T forget the UNITS

16. Calculating with Scientific Notation • Multiplication • Digit terms are multiplied • Exponents are added • Example: • (3.4 x 106 cm)(4.2 x 103 cm) = • (3.4 cm)(4.2 cm) x 10(6+3) = 14.28 x 109 cm2 • = 1.4 x 1010 cm2 • Answer must be rounded correctly DON’T forget the UNITS

17. Calculating with Scientific Notation • Multiplication • Digit terms are divided • Exponents are subtracted • Example: • (3.2 x 103 g)/(5.7 x 10-2 g/mol) = • (3.2 g)/(5.7 g/mol) x 10(3-(-2)) = 0.561 x 105 mol • = 5.6 x 104 mol • Answer must be rounded correctly DON’T forget the UNITS

18. y y x x Proportions • Direct Proportion • Inverse Proportion