Checking a number in under a minute

You cannot recompute everything, so check structurally

Recomputing an answer defeats the purpose. What you can do is apply three or four structural checks that catch most wrong numbers without doing the work again.

1. Order of magnitude

Is it roughly the size it should be? Most serious numerical errors are not small: they are factors of ten, currency mix-ups, thousands read as units, monthly reported as annual.

Estimate crudely before you look. Fourteen staff, average salary around 60,000, so payroll is around 840,000, so an answer of 84,000 or 8.4 million is wrong before you check anything else. This takes five seconds and catches the errors that matter most.

2. Do the parts add up

If you have components and a total, add the components. If percentages are given, do they sum to 100; and if not, is the reason stated? If a table has a total row, check one column.

This is called cross-footing in accounting, it is centuries old, and it catches both extraction errors and arithmetic errors without knowing anything about the subject.

3. Check the units and the basis

The most common silent error in everyday work is not arithmetic. It is a basis mismatch:

• Monthly against annual.
• Net against gross, VAT-inclusive against exclusive.
• Per person against total.
• Calendar year against financial year.
• Two currencies, or one currency at two dates.

Ask explicitly: what is the basis of each figure, and are they the same? A model comparing an inclusive quote with an exclusive one will produce a clean comparison of two things that are not comparable, and nothing in the output will look odd.

4. Trace one number to source

Pick one figure (ideally the one carrying the conclusion) and find it in the original document. Not the total; a component. If that one is right, the extraction was probably working; if it is wrong, everything is suspect.

Choose from the middle or the end of a long extraction, since quality drifts towards the end of a long generation.

Make the checks cheap in the prompt

You can have most of this produced for you:

For every figure: give the value, the source (document and line), the basis (monthly/annual, inclusive/exclusive of tax, currency), and show the arithmetic for anything derived. Add a final line: do the components sum to the total?

Now checking is reading a column rather than recomputing anything.

And for anything calculated, the earlier lesson applies: ask for code or a spreadsheet formula rather than a number, so the arithmetic is performed rather than generated.

Percentages, which deserve their own warning

Percentage change is where people are most often misled, and models reproduce the ambiguity faithfully because it exists in ordinary language.

• Percentage points versus per cent. A rate moving from 4% to 6% is a rise of two percentage points and a rise of 50%. Both statements are true and they sound very different.
• Direction matters. A fall from 100 to 80 is 20% down; going back from 80 to 100 is 25% up. Not symmetric.
• Percentage of what. “30% higher margin” is meaningless without the base.

Ask for the two raw numbers alongside any percentage. That single habit removes most of the confusion, and it removes the possibility of a technically true statement that misleads you.

The honest limit

None of this makes a number right. It catches the wrong ones that have a visible signature: wrong magnitude, inconsistent parts, mismatched basis, untraceable source.

A figure that is subtly wrong, internally consistent, correctly based and traceable to a document that is itself wrong will pass every check here. That is why the last question in this module is about consequence: for a number that could cost you seriously, the check is not a better prompt but a second, independent source.

The thirty-second routine

For any answer with numbers in it that you intend to use:

1. Estimate the headline figure crudely in your head before reading it.
2. Add the components; see whether they make the total.
3. Ask what basis each figure is on, and whether they match.
4. Trace one middle-of-the-list component to the source document.

Four steps, well under a minute, and between them they catch magnitude errors, extraction errors, basis mismatches and drift. Everything left over is a subtle error, and subtle errors are rarer than the four kinds above by a wide margin.