I II III III. Using Measurements (p ) CH. 2 - MEASUREMENT

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

Let’s use a golf analogy

Accurate?No Precise?Yes

Accurate?Yes Precise?Yes

Precise?No Accurate? No

Accurate?Yes Precise?We can’t say!

Dart Example

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

B. 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. % error = 2.9 %

Your Turn  What is the percent error for a mass measurement of 17.7 g, if the correct value is 21.2 g?  A volume is measured experimentally as 4.26 mL. What is the percent error, given the correct value is 4.15 mL?

Error in Measurement  Some error or uncertainty always exists in any measurement.  skill of the measurer  conditions of measurement  measuring instruments

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  Trailing zeros without a decimal point -- 2,500

, C. Significant Figures Counting Sig Fig Examples , sig figs 3 sig figs 2 sig figs

C. 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

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 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

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 5. (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

D. Scientific Notation  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. 65,000 kg  6.5 × 10 4 kg

D. 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

D. Scientific Notation  Calculating with Sci. 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: