A person measures the length and width of a surface as: 45.64 cm and 25.45 cm. Each of these measurements had an uncertainty 0.04 cm. Based on this, what is the range of answers possible for the area of this surface? Give the highest possible measurement and lowest possible measurement, and the expected measurement.

Question

anonymous · Answer

Consider that the lowest value with a 0.04cm variance for the length is 45.60cm (note the 0. It counts as a significant Figure) and 25.41cm for the width. Area is width * length.
Lowest possible:
$$45.60cm*25.41cm=1159cm^2$$
The highest possible length is 45.68cm and the highest width is 25.49cm.
Highest possible:
$$45.68cm*25.49cm=1164cm^2$$
So the range of possible area is from 1159cm^2-1164cm^2.
Our actual expected value is:
$$45.64cm*25.45cm=1162cm^2$$