# Significant digits in context

Sunday 24 April 2016

A teacher has asked about a possible problem following an IB question that appeared on a past paper where a volume of 500 cm^{3} is quoted. The question asked by the teacher is; “Does a volume of 500 cm^{3} imply three significant digits (or figures) or just one significant digit when given in an IB question?”

The easy way the IB could avoid this problem is to use scientific notation, i.e. quote the volume as either 5 x 10^{2} cm^{3} or 5.00 x 10^{2} cm^{3} then it is clearly being quoted to one or three significant digits respectively.

However what is a student supposed to do if the IB writes 500 cm^{3} in a question? This is a pertinent question to ask because it can affect how many significant digits should be given in the answer. If just mathematics is used to argue the case then the answer is clear. 500 is one significant digit. For example, an exact volume of 474 cm^{3} would be quoted as 500 cm^{3} to one significant digit.

The problem as I see it is that the mathematics should not be divorced from the chemistry and the answer actually depends upon how the volume was arrived at in the first place. If some solid was dissolved in water, the resulting solution transferred to a 500 cm^{3} volumetric flask and the total volume made up the mark on the flask, then to me the volume of 500 cm^{3} should be taken as being to three significant digits since a volumetric flask is that accurate. On the other hand, if a 600 cm^{3} beaker was used and the volume of 500 cm^{3} achieved by making up to the 500 cm^{3} mark on the beaker, then the 500 cm^{3} would only probably be accurate to one significant digit.

What I hope this illustrates is that we should be training students to look critically at all the information given not just follow one particular line of reasoning without question. In fact all this emphasis that some teachers put on significant figures is somewhat redundant when it comes to the external assessment. For the past few years, unless specifically asked to give the correct number of significant digits, students have not been penalized in exams if they quote their answers to the wrong number of significant digits.

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