Observations and Measurements

The Nature of Observation Subjective vs. Objective Qualitative vs. Quantitative

Subjective vs. Objective “ I can tell he ’ s lying. ” “ His galvanic skin response changed significantly when he said that. ” Both are valid Both are useful Objective measures usually have more credibility because they are more reproducible

Qualitative vs. Quantitative “ It ’ s really hot outside. ” “ The outside thermometer indicates 35 ºC. ” Both are valid Both are useful Quantitative measures, like objective measures, are considered more credible.

Combinations Subjective Qualitative: –“ Sure is hot! ” Objective Qualitative: –“ The engine light is on. ” Subjective Quantitative: –“ I estimated her speed to be 55 mph. ” Objective Quantitative: –“ RADAR indicated she was traveling at 54 mph.

Quantification: Precision vs. Accuracy Precision: –Scale of measurement –Limited by the instrument Accuracy: –Correctness of measurement –Also limited by the instrument

How precise is the meter stick above? –0.1 cm (or m) –How did we determine this? How accurate is it?

Precise but inaccurate Accurate but imprecise Precise and accurate

Significant Figures Significant Figures indicate the precision with which a measurement has been made –e.g. 1.3 meters has 2 significant digits, indicating that the measurement device could measure tenths of meters, but not hundredths But there can be ambiguity; e.g. –Given 112,000 miles, how many of the digits are significant? –Are any of the zeroes “ real ” ?

Scientific Notation Scientific Notation removes the ambiguity: –1.12 x 10 5 miles has 3 significant digits –1.120 x 10 5 miles has 4 significant digits, and indicates one of the zeroes was “ real ” i.e. we know that it isn ’ t x 10 5 miles but we don ’ t know whether it might be x 10 5 miles or x 10 5 miles

Reporting Results We never report a result with more significant digits than the LEAST significant of the measurements that went into it; e.g. –(1.2 x 10 2 m)(2.15 x 10 0 m) = 2.6 x 10 2 m 2 Some quantities have infinite precision: –If the problem says to “ double ” something, we assume the 2 used to multiply has infinite SFigs –Counts have infinite SFigs Use all in calculation, then round