Estimation and Limits of Accuracy — Solutions
Full worked solutions, with method and final answer for every part.
Question 1
(a)Keep the first 2 significant digits, rounding based on the next digit (1, so round down).
3.1
Question 2
(a)With rounding to the nearest whole unit, the true value lies within half a unit either side.
Lower bound = 11.5 cm, upper bound = 12.5 cm
Question 3
(a)Add half of 0.1 (0.05) to each measurement to get its upper bound, then multiply.
Upper bounds: 8.45 cm × 5.25 cm = 44.3625 cm²
Question 4
(a)Keep the first 2 significant digits (4 and 5), the following digit rounds up.
0.046
Question 5
(a)Add/subtract half of the smallest unit (0.05) to the value.
Lower bound = 3.45 cm, upper bound = 3.55 cm
Question 6
(a)Round each to 1 s.f.: 198→200, 51→50, then multiply.
200 × 50 = 10 000
Question 7
(a)Lower bound of each measurement (subtract 0.05 cm), then multiply.
5.95 × 3.95 ≈ 23.5 cm² (3 s.f.)
Question 8
(a)Look at the third decimal digit (8), which rounds the second digit up.
6.30
Question 9
(a)Rounding every value up moves further from the true answer than necessary; a good estimate rounds each number to the nearest convenient value (up or down), not always in the same direction, to keep errors from compounding.
Always rounding up biases the estimate too high — rounding to the nearest convenient value in either direction gives a fairer estimate
Question 10
(a)Add 0.05 to each measurement for its upper bound, then multiply.
8.45 × 5.25 = 44.3625 cm² ≈ 44.4 cm²
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