Using significant figures
Mathematicians are quite happy to talk about exact numbers however big or small, but in Science a measurement stated as part of the results of a scientific experiment can NEVER be exact. In experimental work across all of the three science subjects, students will be expected to take measurements and record data that is appropriate to the context and apparatus used. The use of digital dataloggers and the processing of data such as the calculation of averages can lead to some common errors with inappropriate use of significant figures. This can also be compounded by challenges with their appreciation of the ideas around accuracy and precision.
It would not be unusual to see a student to produce a results table that contains three time readings of 2.5s, 2.6s and 2.8s and then an average time of 2.63333s without any awareness of the implication of the increased number of significant figures in the average figure provided.
In the mathematics classroom student will meet decimal places but this not be what is most useful in terms of scientific accuracy. In Science significant figure are used to more correctly state the accuracy of a result. If this difference is not discussed with students it may cause misunderstanding to develop.
Make sure students do not drop zeros and hence the place value of the digits. For example 78602 to 2 significant figures is 79000 NOT 79. If this is a problem discuss the role of 0 as a place holder. Again using significant figures in the context of the Science classroom gives them the opportunity to discuss the “sense” of their answer based on its magnitude.
Significant Figures in Science
A short summary of some of the key ideas and considerations when thinking about significant figures with some well chosen science measurement examples such as taking a volume reading from a beaker, measuring cylinder and burette.
Rounding and Significant Digits
This webpage (continuing over to page 3) considers what it means to round to "an appropriate number of significant digits". Page 2 gives a number of examples during which it discusses the role of 0 as a place holder as well as examples where the 0 is a significant figure. Page 3 discusses how to use significant figures in real contexts using the operations of addition and multiplication. Examples could be adapted to use the particular scientific objective you are working with.
NPL Beginners Guide To Measurement
Whilst it does not deal with significant figures directly, if you wanted to spend some time reading about measurement. accuracy and it’s important in a professional scientific context, this guide from the National Physics Laboratory (NPL) is one of the best places to start. It’s not that short but provides an solid overview of the field of measurement and why some things are important to get right. It contains some really nice examples such as why NASA’s Mars Climate Orbiter crashed in 1999. This was because the US scientists were working in Imperial Units and the European part of the team were working in metric!