Precision

Precision is the degree of accuracy given for a number or value. Precision is implied by the use of significant figures. A number is given to an accuracy of a number of figures.

The use of implied precision can be a minefield. Spoken numbers need rounding to something like three significant figures; any extremely large or small number should be given in Standard Form.


Decimal Places are counted to the right of the decimal point. Can’t be hard, then, can it?

Standard Form is used to represent large and small numbers in a consistent way. Standard Form shows  one non-zero digit before the decimal point and is then multiplied by a power of ten to indicate the size. Thus the absolute number and the general size have been separated. Rounding is carried out as for significant figures (indicated by sig.fig., SF, s.f., Std Fm), and usually Std Fm requires you to think about both the rounding and the power of ten.


So what is the number two? It depends on the precision you are using: if working to the nearest whole number, ‘two’ is written 1.5 ≤ 2 <2.5, a half either way.


The number 3.14 is implicitly 3 significant figures. Setting the value of g to be 9.8 implies 9.75≤g<9.85 but setting g to be exactly 9.8 is extreme precision. This is one way of arguing that two and two might be five; we tend to assume that integers (whole numbers) are given exactly – if they are not, and we assume one significant figure instead, then two values of say 2.3 add to sufficient to total more than 4.5, and hence round off to five when expressed to only one significant figure.



As I wrote in UK VS PRC, you might measure a room to centimetre precision, because millimetre accuracy is possible, but not appropriate, since the values will vary. Millimetric precision implies a standard of building that is not likely (nor appropriate to the construction industry). It is this appropriateness of use of number that is a target in Britain. One of the smartest targets in education, methinks, as it will turn the nation into a people that can use number.

© David Scoins 2017