The upper bound of the difference between the length of the pencil and the length of the pen, when considering the precision to the nearest centimeter and millimeter, respectively, is 1.75 cm.
To calculate the upper bound for the difference between the length of the pencil and the length of the pen, we need to consider the maximum possible lengths given the level of precision stated for each item. The length of the pencil is rounded to the nearest cm, so the upper bound for its length is 16.5 cm, as the actual measurement could be up to, but not including, 0.5 cm more than the stated length. The length of the pen is rounded to the nearest mm, so its upper bound is 14.75 cm (since 14.7 cm rounded to the nearest mm could be up to, but not including, 0.05 cm more).
The upper bound difference between the pencil and pen lengths can be found by subtracting the upper bound length of the pen from the upper bound length of the pencil: 16.5 cm - 14.75 cm.
Upper Bound Difference = 1.75 cm