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## Using Scientific Measurements

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**Accuracy vs. Precision**• Accuracy – the closeness of a measurement to the correct or accepted value of quantity measured. • Precision – the closeness of a set of measurements of the same quantity made in the same way • 4 darts clustered together = acc or pre?**Percent Error**• Always some error in a measurement • Instrument, limits of measurer, calibrations • % error – calculated by the following formula… • % error = Valueexp – Valueaccx 100 Valueacc**Significant Figures**• Sig figs – all the digits known with certainty plus one final digit, which is somewhat estimated or uncertain • Graduated cylinder example • 42.5 mL - the 5 is the estimated number**Rules for Determining Sig. Figs.**• All non zero digits are significant • No decimal = book end • Decimal = go to 1st non zero and count everything to the right • Exact numbers have infinite significant figures (1m = 1000mm) • Calculators exaggerate precision**Sig. Fig Examples**• How many sig figs are in… • 203000 • 1000.00 • 0.00052 • 0.06400 • 79.810**Significant Figures**• Multiplication and division sig. digs = answer has no more figs. than the msmt. with the least # of sig. figs. 12.257 5 #’s x 1.162 4 #’s 14.2426340 4 #’s = 14.24**Significant Figures**• Addition and subtraction = answer has no more numbers to the right of the decimal pt. than the number with the least numbers to the right of the decimal. 3.9 5 2.8 79 + 213.6 220.4 29 = 220.4**Scientific Notation**• 29640000000000000000000 copper atoms in 1 penny • 2.964 x 1022 atoms • 2 Parts to scientific notation • # between 1 and 10 • Power of 10**Scientific Notation**• 0.000000000000003332 kg • 3.322 x 10-15 kg • 1970000000 L • 1.97 x 109 • What is ….. In scientific notation? • 4.58 x 105 • 9.05 x 10-3