The Reliability of Numbers
The number 1 million can mean very different things in different contexts. For instance, if you met a friend who had been away and they told you they saw a lake with “like a million ducks,” and then told you that three more ducks landed on the lake, you would know that there probably weren’t 1,000,003 ducks on the lake but only a lot—“like a million”. By the same token, if someone told you that they counted 999,997 fruit flies over the summer and then found three more, you could be pretty sure that there really were a million fruit flies.
Someone who says “like a million” is telling you by their choice of words that the number is somewhat suspect. Someone who tells you that they counted a specific number of things is using their choice of words to state that the number is reliable. Numbers in science also have varying levels of reliability.
In science, numbers are sometimes the result of counting, but more often, and almost exclusively in chemistry, the result of measurements. It is important to understand that no measurement is perfect and the reliability of the measurment depends on the device used to make the measurement. For instance, bathroom scales often measure to the nearest pound. That is more than accurate enough to let you know how your diet is going, but would be a horrible way for a pharmaceutical company to determine how much medicine to put into a capsule. On the other hand, if you stood on the incredibly precise scales used by pharmaceutical companies your weight would destroy them. Generally speaking, the larger something is, the less precise the measurement device will be.
It is important to distinguish, at this point, between accuracy and precision.