Answers vary. Sample response: The shorter pencil appears to be between 5.3 and 5.5 cm, perhaps 5.4 to the nearest mm, while the longer pencil appears to be 17.7 cm to the nearest mm (it is between 17.6 and 17.8 cm).
Answers vary. Sample response: The estimate is accurate to within 1 mm. For the short pencil, it is more than 5.3 cm and less than 5.5 cm, but it is not possible to tell which is closer. Similarly, the longer pencil is more than 17.6 cm and less than 17.8 cm.
For the shorter pencil, taking 5.4 cm as the measured length, the actual length \(x\) is at least 5.3 cm and at most 5.5 cm. The percent error if \(x\) is as small as possible is \(\frac{0.1}{5.3} \approx 2\%\), and if \(x\) is as big as possible, then the error is \(\frac{0.1}{5.5} \approx 2\%\). The first of these gives the greatest percent error, although they are close. For the longer pencil, the percent error is smaller. The biggest it can be is \(\frac{0.1}{17.7} \approx 0.6 \%\). This makes sense because 0.1 cm is a bigger percentage of the length of the small pencil.

7.9.8 Lesson narrative