Question

Your bedroom has a rectangular shape and you want to measure its size. You use a tape that is precise to 0.001 m and find that the shortest wall in the room is 3.547 m long. The tape, however is too short to measure the length of the second wall, so you use a second tape, which is longer but only precise to 0.01 m. You measure the second wall to be 4.79 m long. Which of the following numbers is the most precise estimate that you can obtain from your measurements for the area of your bedroom?

a. 17.0 m2
b. 16.990 m2
c. 16.99 m2
d. 16.9 m2
e. 16.8 m2

Answer 1

a. 17.0 m²

Step-by-step explanation:

The product of the two dimensions is 16.99013 m². The least precise contributor has 3 significant figures, so the most precise result available is one with 3 significant figures: 17.0 m².

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Additional comment

Given that each measurement may be in error by 1/2 of a least-significant digit, their product can be as little as 16.9700025, or as great as 17.0102625. This amounts to 16.9901325 ± 0.0201300. The value 17.0 suggests a range from 16.95 to 17.05, which exceeds the actual range possible with the given measurements. On the other hand, a 4 significant-figure value (16.99) suggests a much smaller range in the product than there may actually be: (16.985, 16.995)