Problem 5.110 pts) Correct the following reported measurements: a. 33.57 +7.791 b. 45.667x1093.77x10-10 c. 10.20110 + 1.0988 d. 98.6 +0.512 Solution: a. 33.57 + 7.791 as corrected becomes b. 45.667x10 +3.77x10-10 as corrected becomes c. 10.20110 + 1.0988 as corrected becomes d. 98.6 + 0.512 as corrected becomes 123456 + 6543 m 4.996 of nominal 0.4% 0.03% 0.002% measurement is 123500 6500 meters, Figure 1.8 Comparison of Magnitudes of the Digits in an Uncertainty. 2. The nominal value of a measurement and its uncertainty should usually be written to the same decimal place. This rule extends naturally from the previous rule: Consider again the measurement 1234567 Since the uncertainty in the measurement is, at best, to the 100 place, then it makes no sense to Since meters. Correcting its uncertainty, this measurement is expressed as 123456 = 6500 meters report the nominal value to any greater accuracy. Thus the appropriate way to report this addition/subtraction rule for significant figures of Section 3.2. That is, if we add or subtract the (Note that this format is consistent with the uncertainty to the nominal value, we would expect to reduce the digits of the result to match the least accurately-known value.) NOTE: The decimals of the nominal value and the uncertainty do NOT always have to match exactly. Consider the digital reading shown in Figure 1.1a, whose nominal value is 0.30 g. We interpreted the uncertainty as +0.005 g, so the reading should be expressed as 0.30 + 0.005, NOT 0.300 + 0.005. Adding an extra decimal place to the nominal value is misleading, because it gives the mistaken impression that the device was read to three decimal places. 3. For clarity, use the same notation (scientific or standard) for nominal values and uncertainties. Examples: a. 1.234x10 + 300 m should be written as (1.234+0.003)x10 m or 123400 +300 m. b. 5.68x10' + 3x10 kg should be written as (5.68 +0.03)x10 kg. c. (213.01 +0.23) 10 m should be written as (2.1301 +0.0023) x 10 m. (Scientific notation always places the decimal after the first digit.)