Measurements

How many Decimal Places?

Suppose you have a timer which measures to a precision of 0·01s and it gives a reading of 4·58s. The actual time being measured could have been 4·576s or 4·585s etc. However, we have no way of knowing this, so we write

t = 4·58s ± 0·01s

If we now repeat the experiment using a better timer which measures to a precision of 0·0001s. The timer might still give us a time of 4·58s but now we would indicate the greater precision of the instrument being used by stating the result as

t = 4·5800s ± 0·0001s

So, as a general rule, look at the precision of the instrument being used and state the result to that number of decimal places.

Another point to remember is that very often we will be using our results to plot a graph. On most graph paper you can represent a result to a precision of 3 significant figures (3 sig. fig.). So (assuming that your measurements allow for this level of precision) convert your table of results to lists of numbers in standard form and give them to two decimal places. (By "standard form" we mean a number between 0·00 and 9·99 multiplied by the appropriate power of 10.)

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