Uncertainty in Measurements Uncertainties always exist in measured quantities. Measured quantities are generally reported in such a way that only the last digit is uncertain. Precision and Accuracy are two closely related terms with uncertainties of measurements. Accurate: Ex. Precise: Ex. To see the difference imagine that you weight a tennis ball, whose true mass is 54.44178 g, on three different types of balances. Measurement Balance Bathroom Scale Lab Balance Analytical 1 0.0kg 54.4g 54.4419g 2 0.0kg 54.7g 54.4417g 3 0.1kg 54.1g 54.4417g Average 0.03kg 54.4g 54.4418g To indicate the uncertainty in a measurement, the value you record should use all the digits you are sure of, plus one additional digit that you estimate. Significant Figures The total number of digits in a measurement is called the significant figures. More number of significant figures in a measurement less uncertain the measurement is. RULES: *Non zero integers always count as significant figures. Ex. 234 or 1768 *Zeros present in a measured quantity present problems (to find the number of significant figures) because they can be used in two ways: as part of the measured value or to position a decimal point. • Zeros between two other significant digits (enclosed zeros or captive zeros) are always significant. Ex. 1107 or 50.001 • Zeros at the beginning (leading zeros) of a number are never significant. Ex. 0.0025 or 0.02 • Zeros at the end (trailing zeros) of a number are significant if they involve a decimal point. They are the zeros at the right end of the number. Ex. 0.0500 or 3.00 or 100. *Rules also apply to scientific notation! *Exact Numbers= Often calculations involve numbers that were not obtained using measuring devices but were determined by counting. Such numbers are assumed to have an unlimited number of significant figures. Exact numbers also arise from definitions. Exact numbers do not limit the number of significant figures in calculations. Ex. 1 in = 2.54 cm or 3 apples. chemisTRY: How many significant figures are in the following? 1. 1107 km 2. 0.764 g 3. 0.000127 cm 4. 0.3000 g 5. 0.050120 kg 6. 4000 m 7. 2.0800 x 10 2 L 8. 480 m 9. 480 cars 10. 0.0108 g