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 theres 1 digit to its left. Places moved = exponent. Large # (>1) positive exponent Small # (