Significant Figures.

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Presentation transcript:

Significant Figures

Uncertainty in Measurements There are two types of uncertainty associated with a measurement: Accuracy: Agreement of the measured value with the true value. Precision: Agreement among repeated measurements.

Example Measured mass of an object with true mass 2.65 g. Measurement Method 1 Method 2 1 2.64 2.94 2 2.67 2.61 3 2.65 2.44 4 2.67 2.76 average 2.66 2.69 error 0.01 0.04 spread 0.03 0.50

Significant Figures Assumes an uncertainty of ±1 in the last measured digit. The greater the number of significant digits, the smaller the relative uncertainty. Example: The mass of a penny: Balance Mass Uncertainty Fisher S400 3.12 g 0.32% Ohaus GT210 3.117 g 0.032% Mettler 100 3.1169 g 0.0032%

Counting Significant Digits The number of digits from the first nonzero digit to the last digit. Exception: With no decimal point, zeros at the end of a number may or may not be significant. 0.0205 has 3 sig. figs. 1045.010 has 7 sig. figs. 10130 has 4 or 5 sig. figs. 1.013x104 has 4 sig. figs. 1.0130x104 has 5 sig. figs.

Uncertainty in Calculations There are two rules for the number of significant digits in calculated numbers: Multiplication and Division The result has the same number of significant digits as the number with the fewest significant digits. Addition and Subtraction The result has the same number of decimal places as the number with the fewest decimal places.

Examples 3.141  6.7104 = 2.1105 27.5 + 273.15 = 300.6 9.1300  31 = 0.29 71.2238 - 38.24 = 32.98

Exact Numbers Some numbers are not measured and have no uncertainty. Counting numbers - Obtained by counting whole objects. 10 protons in a nucleus means 10.000... Defined numbers - Some quantities are defined exactly: 1 ft = 12 in 1 L = 103 mL 1 in = 2.54 cm Hypothetical numbers - Usually spelled out: a, one, etc.