How to use numbers correctly in writing

Using Numbers in Text

In arithmetic, book-keeping, and sometimes in accounting, numbers are absolute, that is, they mean exactly what they say. But in most fields, this does not apply. There is an element of implication by the writer and interpretation by the reader. So, we have to be careful to use numbers correctly. In particular, we have to understand the meaning of 'significant figures' to make sure our numerical examples don't discredit our written work. Here is a beginner's guide to Significant Figures:

Let's start with an obvious statement: a number is not another number, e.g.

7 is not the same as 6 or 8

7.3 is not the same as 7.2 or 7.4

This is telling us something vital:

A number carries two pieces of information:

  • an explicit value
  • an implicit precision

This means we should avoid implying a higher precision than the facts justify. We should also avoid presenting numbers with a higher precision than the reader needs. As an example, compare the following:

  1. The typical monthly rate is $7,000
  2. The typical monthly rate is £4,376

What has happened here is that the perfectly reasonable $7,000 has been converted to Sterling at the prevailing exchange rate of 1.599, resulting in what is actually a nonsense statement. It is perfectly possible that nobody receives the precise rate of £4,376, so it can't be described as typical. This is an example of false precision. Here's another:

  1. He's reckoned to be a 90 mph pitcher.
  2. He's reckoned to be a 40.234 m/s pitcher

When we describe someone as a 90 mph pitcher we're saying that he can be reliably expected to deliver the ball round about 90 mph. Round about 90 mph converts to round about 40 m/s, not to 40.234, which is ludicrously over-precise for the context.

Recipes often suffer the same fate in translation, with half a pint or 8 ounces turning into the frightening 23.7 centilitres or 227 grams, quantities that could only be measured with laboratory equipment. (The correct approach, of course, is to write a new metric recipe, rather than convert the old units).

Significant Figures

Significant Figures is the technical name for what we are talking about. The idea is simple enough: The least significant (furthest right) non-zero digit should be known to be accurate within fixed limits.

Examples:

17m (million) really means -

a number between 16.5m and 17.5m

The following numbers are all expressed to the same precision (3 significant figures):

  1. 10,500
  2. 217
  3. 5.89
  4. 7.30
  5. 0.00378

Notice the fourth one, 7.30. The last zero shows that the precision is 3 significant figures, i.e. the range is from 7.295 to 7.305 If you omit it, the precision is only 2 significant figures and the range is far wider, from 7.25 to 7.35.

This has only been an introduction to a much bigger field. The important point, though, is just to make sure your numbers are presented with precision appropriate to the context, that is, with the correct number of significant figures.

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