Question

Using a common metric ruler, you measure the separation distance between two al spheres from center to center to be 2.3 cm. What is the lowest uncertainty that you can use with this measurement?

Answer 1

The lowest uncertainty for a measurement of 2.3 cm using a metric ruler with millimeter markings would be ±0.05 cm, considering that the estimated uncertainty is half of the ruler's smallest division.

Step-by-step explanation:

When measuring the separation distance between two al spheres using a common metric ruler, the lowest uncertainty that one can report is typically determined by the smallest division on the ruler. If the ruler has millimeter markings, which are tenths of a centimeter (0.1 cm), then the measurement can be read to the nearest tenth and an additional estimated digit. Therefore, if a measurement reads 2.3 cm on such a ruler, the first two digits (2 and 3) are certain and the third digit can be estimated. The estimated digit, or uncertainty, is typically half of the smallest division on the ruler, in this case, ±0.05 cm, because you can reasonably estimate whether the measurement falls in the middle of the two markings.

This means that if you measure the distance as 2.3 cm, your recorded measurement with the lowest possible uncertainty would be 2.30 ± 0.05 cm. This measurement acknowledges that there is a small degree of potential variation or error even when using a precise measuring tool like a metric ruler with millimeter markings.