Chapter 2 - Section 3 Suggested Reading Pages Using Scientific Measurements

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

Neither

Precision

Accuracy & Precision

Percent Error  Indicates accuracy of a measurement experimental value – accepted value accepted value X 100 % Error =

Making Measurements  Write down all certain or exact digits you can read off the instrument, AND one more estimated digit.  Measuring always involves some estimation.

*Uncertainty  Estimate the last digit  Uncertainty is plus-or-minus based on the estimated digits place.  The ratio of the estimated uncertainty to the smallest scale division depends on the separation between the markings.

 Left: 1.5 ± 0.5 inches  Right: 1.48 ± 0.01 inches

 30.0 ± 0.1 degrees C

 Read at the bottom of the meniscus  4.86 ± 0.01 ml

 Try to read these and estimate uncertainty correctly.

 Left: 5.75 ± 0.01 mL

 Middle: 3.0 ± 0.5 mL

 Right: 0.35 ± 0.05 mL

*Mercury Meniscus is inverted

Significant Figures  Indicate precision of a measurement.  Recording Significant Figures  Significant figures in a measurement include the known digits plus a final estimated digit 2.32 cm

Counting Significant Figures  Count all numbers EXCEPT:  Leading zeros  Trailing zeros without a decimal point -- 2,500

, Significant Figures Significant Figures Examples: , sig figs 3 sig figs 2 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 Sig Fig Rules

 Add/Subtract - The # with the fewest digits to the right of the decimal place determines the place of the last sig fig in the answer mL mL 7.85 mL  7.9 mL 3.75 mL mL 7.85 mL

Significant Figures  Add/Subtract – working with whole numbers, round so the final sig fig is in the same place as the leftmost uncertain digit. 224 g g 354 g  350 g 224 g g 354 g

Significant Digits  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

Significant Digits 5. (15.30 g) ÷ (6.4 mL) Practice Problems = g/mL  18.1 g g g g 4 SD2 SD  2.4 g/mL 2 SD

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 significant digits. 65,000 kg  6.5 × 10 4 kg

Practice Problems 7. 2,400,000  g kg 9.7  km  10 4 mm 2.4  10 6  g 2.56  kg km 62,000 mm = = = =

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:

Proportions  Direct Proportion  Inverse Proportion y x y x

Percent  A fraction can be written as a percent by converting it to a decimal and then multiplying by 100.  Ex: 900 million kilograms of plastic soda bottles are produced each year. 180 million kilograms of them are recycled. 900 million kg = 0.2 x 100% = 20% 180 million kg