Jennifer and Maury calculated the averages and SDMs for several types of measure

Question

Jennifer and Maury calculated the averages and SDMs for several types of measurements. They got into a rote mood and copied all the digits that appeared on their scientific calculator. Please boil these down to the “correct” number of significant figures and state how many significant figures is being reported for each best estimate.

(a) 82.34677662 ± 0.072314389 degrees Celsius

(b) 282.5723 ± 2.31684 seconds

(c) – 0.0373749738 ± 0.005174523 Volts

(d) 7648.78349 ± 258.549763 meters (express this answer with and without scientific notation)

(e) Explain why the result of rounding off in part (d) is ambiguous unless scientific notation is used.

Explanation / Answer

a)

82.35 ± 0.07) = (8.235 ± 0.007) x 101.degree Celsius
Number of significant digits = 3. We know only the digits 82.3 for sure, there is an error in estimating the next digit.

b)

(283 ± 2) s = (2.83 ± 0.02) x 102) s
Number of significant digits = 2. The final value comes in the range of 280 to 284 s and since the last digit is not certain, the number of significant digits are 2.

c)

(- 0.037 ± 0.005) V = (- 3.7 ± 0.5 x 10-2) V
Number of significant figures = 2, this is .03

d)

7649 ± 259 = (7.649 ± 0.259 x 103 ) m
Number of significant figures = 1

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