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

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.

There is a lot of fuss made about using the appropriate level of precision and so there should be. If you estimate a rate as about 3 things in about 7 units, that does not give you 6 figure accuracy (0.428571) in your answer. Even two might be misleading, (0.43).

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. While precision is defined as the number of digits, ‘two’ is only using a single digit, so unless it is clear that we are counting in integers (no decimal parts at all), such as counting people or cars, then we must recognise the vagueness, the lack of precision in a single digit representation.

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.

There is a growing terminology (that is, I have seen it recently but had never seen it before) that says 12.345 had a scale of 3 and a precision of 5. Five significant gigures, two after the decimal point.

Precision v Accuracy See.

Strictly, precision is the number of digits you give for a number, while accuracy is correctness. Calling pi 22/7 is correct to 3 sig.fig and at that precision it is accurate. 3.142857 =22/7 has 7 figure precision but us not accurate for pi, which is 3.14159265 to the precision used.  Out simply, more precision, means more digits but it might well be inaccurate and therefore not actually correct. 

The longer version of a number contains more information and this is what is called more precision. Unfortunately we don’t learn this word correctly, because there is a point where the extra precision, the additional information, is unhelpful and even misleading. Suppose you’re trying to calculate how to his a target and you have a number of numbers that indicate how to achieve that. You only want to hit the target, so the level of precision that hits the centre of the target to within some small margin of error is actually not helpful; what you really want is the figures at the right level of precision to hit the target, any part of it. 

From the link above: The standard example I always heard involved a dart board:

  • accurate but not precise: lots of darts scattered evenly all over the dart board
  • precise but not accurate: lots of darts concentrated in one spot of the dart board, that is not the bull's eye
  • both: lots of darts concentrated in the bull's eye

Accuracy is about getting the right answer. Precision is about repeatedly getting the same answer.

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