{"course":{"slug":"prompting","title":"Getting Real Work out of a Model","url":"https://addaly.com/learn/prompting","level":"beginner","track":"start"},"lesson":{"slug":"checking-numbers","title":"Checking a number in under a minute","url":"https://addaly.com/learn/prompting/checking-numbers","position":59,"of":72,"minutes":8,"answer":"Check a number by magnitude, by whether the parts add up, by whether the bases match, and by tracing one component to its source; and ask for the two raw numbers behind any percentage.","keyIdea":"Check a number by magnitude, by whether the parts add up, by whether the bases match, and by tracing one component to its source; and ask for the two raw numbers behind any percentage."},"body":{"format":"markdown","text":"## You cannot recompute everything, so check structurally\n\nRecomputing 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.\n\n## 1. Order of magnitude\n\nIs 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.\n\nEstimate 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.\n\n## 2. Do the parts add up\n\nIf 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.\n\nThis 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.\n\n## 3. Check the units and the basis\n\nThe most common silent error in everyday work is not arithmetic. It is a basis mismatch:\n\n- Monthly against annual.\n- Net against gross, VAT-inclusive against exclusive.\n- Per person against total.\n- Calendar year against financial year.\n- Two currencies, or one currency at two dates.\n\nAsk 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.\n\n## 4. Trace one number to source\n\nPick 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.\n\nChoose from the middle or the end of a long extraction, since quality drifts towards the end of a long generation.\n\n## Make the checks cheap in the prompt\n\nYou can have most of this produced for you:\n\n> 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?\n\nNow checking is reading a column rather than recomputing anything.\n\nAnd 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.\n\n## Percentages, which deserve their own warning\n\nPercentage change is where people are most often misled, and models reproduce the ambiguity faithfully because it exists in ordinary language.\n\n- **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.\n- **Direction matters.** A fall from 100 to 80 is 20% down; going back from 80 to 100 is 25% up. Not symmetric.\n- **Percentage of what.** \"30% higher margin\" is meaningless without the base.\n\nAsk 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.\n\n## The honest limit\n\nNone of this makes a number right. It catches the wrong ones that have a visible signature: wrong magnitude, inconsistent parts, mismatched basis, untraceable source.\n\nA 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.\n\n## The thirty-second routine\n\nFor any answer with numbers in it that you intend to use:\n\n1. Estimate the headline figure crudely in your head before reading it.\n2. Add the components; see whether they make the total.\n3. Ask what basis each figure is on, and whether they match.\n4. Trace one middle-of-the-list component to the source document.\n\nFour 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."},"check":{"question":"A model compares two supplier quotes and reports that Supplier A is 12% cheaper. Which check is most likely to overturn the conclusion?","options":[{"text":"Recomputing the 12% from the two totals.","correct":false,"tempting":"Verifies the arithmetic on figures that may not be comparable in the first place."},{"text":"Asking the model how confident it is in the comparison.","correct":false,"tempting":"Stated confidence carries no information about correctness."},{"text":"Checking that both quotes were read in full.","correct":false,"tempting":"Worth doing, but a complete reading of two differently based quotes still produces an invalid comparison."},{"text":"Confirming that both totals are on the same basis: same tax treatment, same currency, same delivery terms, same quantity.","correct":true}]},"prev":{"slug":"claims-about-a-document","title":"Checking a claim about a document you have","url":"https://addaly.com/learn/prompting/claims-about-a-document"},"next":{"slug":"the-sycophancy-trap","title":"Disagreeing without getting agreement","url":"https://addaly.com/learn/prompting/the-sycophancy-trap"},"authorship":"Founder and series editor: Dr Mustafa Mun. Written by AI models to a written standard. Exam keys checked blind by a second model: 3,665 of 3,666 agreed. Academic review invited.","review":{"status":"Draft, open for academic review"},"cite":"Addaly (2026) 'Checking a number in under a minute', in Getting Real Work out of a Model. Edited by M. Mun. Addaly. Available at: https://addaly.com/learn/prompting/checking-numbers (Accessed: 13 October 2026).","licence":{"name":"CC BY-NC-SA 4.0","url":"https://creativecommons.org/licenses/by-nc-sa/4.0/"},"reader":{"schema":1,"title":"Checking a number in under a minute","courseTitle":"Getting Real Work out of a Model","module":{"index":7,"slug":"checking-the-answer","title":"Checking the answer"},"answer":null,"keyIdea":"Check a number by magnitude, by whether the parts add up, by whether the bases match, and by tracing one component to its source; and ask for the two raw numbers behind any percentage.","hero":{"kind":"plate","image":"https://addaly.com/art/modules/prompting/checking-the-answer.webp","alt":"A clinic reception desk with a rubber stamp, a ruled sheet, spectacles, an open book and a telephone.","caption":"Verification is a desk habit rather than a feeling: the claim, the register it is checked against, and the stamp that only goes on afterwards."},"blocks":[{"t":"h2","id":"you-cannot-recompute-everything-so-check-structurally","runs":[{"text":"You cannot recompute everything, so check structurally"}]},{"t":"p","runs":[{"text":"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."}]},{"t":"h2","id":"1-order-of-magnitude","runs":[{"text":"1. Order of magnitude"}]},{"t":"p","runs":[{"text":"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."}]},{"t":"p","runs":[{"text":"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."}]},{"t":"h2","id":"2-do-the-parts-add-up","runs":[{"text":"2. Do the parts add up"}]},{"t":"p","runs":[{"text":"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."}]},{"t":"p","runs":[{"text":"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."}]},{"t":"h2","id":"3-check-the-units-and-the-basis","runs":[{"text":"3. Check the units and the basis"}]},{"t":"p","runs":[{"text":"The most common silent error in everyday work is not arithmetic. It is a basis mismatch:"}]},{"t":"ul","items":[[{"text":"Monthly against annual."}],[{"text":"Net against gross, VAT-inclusive against exclusive."}],[{"text":"Per person against total."}],[{"text":"Calendar year against financial year."}],[{"text":"Two currencies, or one currency at two dates."}]]},{"t":"p","runs":[{"text":"Ask explicitly: "},{"text":"what is the basis of each figure, and are they the same?","b":true},{"text":" 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."}]},{"t":"h2","id":"4-trace-one-number-to-source","runs":[{"text":"4. Trace one number to source"}]},{"t":"p","runs":[{"text":"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."}]},{"t":"p","runs":[{"text":"Choose from the middle or the end of a long extraction, since quality drifts towards the end of a long generation."}]},{"t":"h2","id":"make-the-checks-cheap-in-the-prompt","runs":[{"text":"Make the checks cheap in the prompt"}]},{"t":"p","runs":[{"text":"You can have most of this produced for you:"}]},{"t":"quote","runs":[{"text":"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?"}]},{"t":"p","runs":[{"text":"Now checking is reading a column rather than recomputing anything."}]},{"t":"p","runs":[{"text":"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."}]},{"t":"h2","id":"percentages-which-deserve-their-own-warning","runs":[{"text":"Percentages, which deserve their own warning"}]},{"t":"p","runs":[{"text":"Percentage change is where people are most often misled, and models reproduce the ambiguity faithfully because it exists in ordinary language."}]},{"t":"ul","items":[[{"text":"Percentage points versus per cent.","b":true},{"text":" 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."}],[{"text":"Direction matters.","b":true},{"text":" A fall from 100 to 80 is 20% down; going back from 80 to 100 is 25% up. Not symmetric."}],[{"text":"Percentage of what.","b":true},{"text":" “30% higher margin” is meaningless without the base."}]]},{"t":"p","runs":[{"text":"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."}]},{"t":"h2","id":"the-honest-limit","runs":[{"text":"The honest limit"}],"role":"limit"},{"t":"p","runs":[{"text":"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."}]},{"t":"p","runs":[{"text":"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."}]},{"t":"h2","id":"the-thirty-second-routine","runs":[{"text":"The thirty-second routine"}]},{"t":"p","runs":[{"text":"For any answer with numbers in it that you intend to use:"}]},{"t":"ol","start":1,"items":[[{"text":"Estimate the headline figure crudely in your head before reading it."}],[{"text":"Add the components; see whether they make the total."}],[{"text":"Ask what basis each figure is on, and whether they match."}],[{"text":"Trace one middle-of-the-list component to the source document."}]]},{"t":"p","runs":[{"text":"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."}]}],"check":{"question":[{"text":"A model compares two supplier quotes and reports that Supplier A is 12% cheaper. Which check is most likely to overturn the conclusion?"}],"options":[{"text":[{"text":"Recomputing the 12% from the two totals."}],"correct":false,"tempting":[{"text":"Verifies the arithmetic on figures that may not be comparable in the first place."}]},{"text":[{"text":"Asking the model how confident it is in the comparison."}],"correct":false,"tempting":[{"text":"Stated confidence carries no information about correctness."}]},{"text":[{"text":"Checking that both quotes were read in full."}],"correct":false,"tempting":[{"text":"Worth doing, but a complete reading of two differently based quotes still produces an invalid comparison."}]},{"text":[{"text":"Confirming that both totals are on the same basis: same tax treatment, same currency, same delivery terms, same quantity."}],"correct":true,"tempting":null}],"order":[2,1,3,0],"why":null},"prev":{"slug":"claims-about-a-document","title":"Checking a claim about a document you have","minutes":8},"next":{"slug":"the-sycophancy-trap","title":"Disagreeing without getting agreement","minutes":8}}}