{"course":{"slug":"ai-for-students","title":"AI for Students","url":"https://addaly.com/learn/ai-for-students","level":"beginner","track":"work"},"lesson":{"slug":"lab-sciences-and-units","title":"The lab sciences, and the dimension check","url":"https://addaly.com/learn/ai-for-students/lab-sciences-and-units","position":32,"of":73,"minutes":8,"answer":"Carry units through every line as algebra and the dimensions will catch most wrong formulae instantly; then apply significant figures and uncertainty yourself, because those are the parts a lab report is actually marked on.","keyIdea":"Carry units through every line as algebra and the dimensions will catch most wrong formulae instantly; then apply significant figures and uncertainty yourself, because those are the parts a lab report is actually marked on."},"body":{"format":"markdown","text":"## Where physics and chemistry problems break\n\nIn a quantitative science, the model's weaknesses land on the parts where marks are actually allocated: the number, the unit, the significant figures, and the assumption that made the calculation legitimate.\n\nThe good news is that these subjects come with the strongest error-detection method in this entire course, and it is free, instant and does not need a computer.\n\n## Dimensional analysis, used properly\n\nCarry the units through every line as though they were algebra. Cancel them. Whatever remains must be the unit of the answer.\n\nThis catches a startling proportion of errors, including most of the ones a generated solution will contain, because a wrong formula usually has wrong dimensions.\n\n> Kinetic energy: half m v squared. kg times (m/s) squared is kg m² s⁻², which is a joule. Correct.\n>\n> If a solution produced kg m s⁻², that is a newton, and the error is upstream: a v that should have been v squared, most likely.\n\nDimensional analysis also lets you reconstruct formulae you have forgotten. If you know a period depends on length and gravity, the only combination of metres and m s⁻² giving seconds is the square root of length over g. You have just recovered the pendulum formula without remembering it, up to a constant.\n\nAsk the model to do this deliberately:\n\n> Before giving me a number, show the dimensions of every quantity and confirm the units of the result.\n\n## Significant figures, which are marked and usually wrong\n\nModels routinely give ten decimal places or round to two when the data supported four. Both lose marks. The rules are yours to apply:\n\n- Multiplication and division: the result carries the same number of significant figures as the least precise input.\n- Addition and subtraction: the same number of decimal places as the least precise input.\n- Constants and exact counts do not limit precision.\n- Round once, at the end, not at each step.\n\nThis is a place where a marker can see, in one glance, whether the person understood their measurement or copied a number. It is cheap to get right and it is regularly the difference between full and partial credit.\n\n## Uncertainty, which is the actual physics\n\nA measurement without an uncertainty is not a result. Models handle uncertainty propagation adequately in simple cases and badly in correlated ones, and they will often omit it entirely unless asked.\n\nFor a lab report, do it yourself. The rules for independent uncertainties are short: add absolute uncertainties for sums and differences, add relative uncertainties in quadrature for products and quotients. Ask the model to explain *why* those rules take that form (the derivation from a first-order expansion is worth understanding) and then apply them by hand or in a spreadsheet.\n\nFree tools: LibreOffice Calc or Google Sheets for propagation, **Python with NumPy** for anything larger, and the `uncertainties` package if you want it done automatically.\n\n## Chemistry specifics\n\n- **Balancing equations.** Check every element yourself; a plausible-looking unbalanced equation is common.\n- **Oxidation states and mechanisms.** Reasonable on standard textbook cases, unreliable on anything unusual, and confidently wrong on stereochemistry.\n- **Structures and diagrams.** Text descriptions of molecular geometry are frequently muddled. Draw it. **Avogadro** and **Jmol** are free molecular editors; **ChemDraw** is what industry names, and **ChemSketch** has a free academic version.\n- **Safety information.** Never take a hazard, incompatibility or first-aid answer from a model. Use the actual safety data sheet, which is free and legally required to exist for every reagent in your lab.\n\n## Biology and the currency of specifics\n\nBiology is unusually exposed to the specificity problem: it runs on named genes, named pathways, named species, named studies and constantly-revised guidelines. A model is strong on mechanism at textbook level and unreliable on any of those particulars, especially anything revised since its training.\n\nAnd the standing rule for anything clinical: **do not use it for advice about a real person, including yourself.** Guidelines change, they differ by country, and the model has no way to know your case. Use it to understand a mechanism you are being taught. Ask a clinician about a patient.\n\n## What the model is good at here\n\nExplaining why a formula has the form it has. Building intuition for a concept before the maths. Generating practice problems of a named type. Checking your working for the *first* wrong line. Explaining a paper's methods section. Suggesting what could have caused an anomalous result in your data, as a list of hypotheses for you to test, which is a real and underused move for a discussion section, provided you evaluate the hypotheses rather than reporting them."},"check":{"question":"A student checks a generated solution and finds the units come out as kg m s⁻² where the answer should be in joules. What have they learned?","options":[{"text":"That an error exists upstream: a quantity used to the wrong power or a wrong formula.","correct":true},{"text":"That significant figures were applied at the wrong stage of the calculation.","correct":false,"tempting":"Confuses precision with dimension; rounding never changes what physical quantity a result represents."},{"text":"That the final numerical value needs converting into the correct unit before submission.","correct":false,"tempting":"Treats a dimensional mismatch as a units conversion; newtons and joules differ by a length, so no conversion factor exists between them."},{"text":"That the model used a different but equivalent formulation, since force times distance and energy are dimensionally related quantities in some conventions.","correct":false,"tempting":"Invents a convention; force times distance is energy precisely because the dimensions differ by a length, which is what the missing factor reveals."}]},"prev":{"slug":"programming-and-cs","title":"Code that runs and is wrong","url":"https://addaly.com/learn/ai-for-students/programming-and-cs"},"next":{"slug":"history-and-sources","title":"History, and the quotation that was never said","url":"https://addaly.com/learn/ai-for-students/history-and-sources"},"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) 'The lab sciences, and the dimension check', in AI for Students. Edited by M. Mun. Addaly. Available at: https://addaly.com/learn/ai-for-students/lab-sciences-and-units (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":"The lab sciences, and the dimension check","courseTitle":"AI for Students","module":{"index":4,"slug":"subject-by-subject","title":"Subject by subject"},"answer":null,"keyIdea":"Carry units through every line as algebra and the dimensions will catch most wrong formulae instantly; then apply significant figures and uncertainty yourself, because those are the parts a lab report is actually marked on.","hero":{"kind":"plate","image":null,"alt":null,"caption":null},"blocks":[{"t":"h2","id":"where-physics-and-chemistry-problems-break","runs":[{"text":"Where physics and chemistry problems break"}]},{"t":"p","runs":[{"text":"In a quantitative science, the model’s weaknesses land on the parts where marks are actually allocated: the number, the unit, the significant figures, and the assumption that made the calculation legitimate."}]},{"t":"p","runs":[{"text":"The good news is that these subjects come with the strongest error-detection method in this entire course, and it is free, instant and does not need a computer."}]},{"t":"h2","id":"dimensional-analysis-used-properly","runs":[{"text":"Dimensional analysis, used properly"}]},{"t":"p","runs":[{"text":"Carry the units through every line as though they were algebra. Cancel them. Whatever remains must be the unit of the answer."}]},{"t":"p","runs":[{"text":"This catches a startling proportion of errors, including most of the ones a generated solution will contain, because a wrong formula usually has wrong dimensions."}]},{"t":"quote","runs":[{"text":"Kinetic energy: half m v squared. kg times (m/s) squared is kg m² s⁻², which is a joule. Correct."}]},{"t":"quote","runs":[]},{"t":"quote","runs":[{"text":"If a solution produced kg m s⁻², that is a newton, and the error is upstream: a v that should have been v squared, most likely."}]},{"t":"p","runs":[{"text":"Dimensional analysis also lets you reconstruct formulae you have forgotten. If you know a period depends on length and gravity, the only combination of metres and m s⁻² giving seconds is the square root of length over g. You have just recovered the pendulum formula without remembering it, up to a constant."}]},{"t":"p","runs":[{"text":"Ask the model to do this deliberately:"}]},{"t":"quote","runs":[{"text":"Before giving me a number, show the dimensions of every quantity and confirm the units of the result."}]},{"t":"h2","id":"significant-figures-which-are-marked-and-usually-wrong","runs":[{"text":"Significant figures, which are marked and usually wrong"}]},{"t":"p","runs":[{"text":"Models routinely give ten decimal places or round to two when the data supported four. Both lose marks. The rules are yours to apply:"}]},{"t":"ul","items":[[{"text":"Multiplication and division: the result carries the same number of significant figures as the least precise input."}],[{"text":"Addition and subtraction: the same number of decimal places as the least precise input."}],[{"text":"Constants and exact counts do not limit precision."}],[{"text":"Round once, at the end, not at each step."}]]},{"t":"p","runs":[{"text":"This is a place where a marker can see, in one glance, whether the person understood their measurement or copied a number. It is cheap to get right and it is regularly the difference between full and partial credit."}]},{"t":"h2","id":"uncertainty-which-is-the-actual-physics","runs":[{"text":"Uncertainty, which is the actual physics"}]},{"t":"p","runs":[{"text":"A measurement without an uncertainty is not a result. Models handle uncertainty propagation adequately in simple cases and badly in correlated ones, and they will often omit it entirely unless asked."}]},{"t":"p","runs":[{"text":"For a lab report, do it yourself. The rules for independent uncertainties are short: add absolute uncertainties for sums and differences, add relative uncertainties in quadrature for products and quotients. Ask the model to explain "},{"text":"why","i":true},{"text":" those rules take that form (the derivation from a first-order expansion is worth understanding) and then apply them by hand or in a spreadsheet."}]},{"t":"p","runs":[{"text":"Free tools: LibreOffice Calc or Google Sheets for propagation, "},{"text":"Python with NumPy","b":true},{"text":" for anything larger, and the "},{"text":"uncertainties","code":true},{"text":" package if you want it done automatically."}]},{"t":"h2","id":"chemistry-specifics","runs":[{"text":"Chemistry specifics"}]},{"t":"ul","items":[[{"text":"Balancing equations.","b":true},{"text":" Check every element yourself; a plausible-looking unbalanced equation is common."}],[{"text":"Oxidation states and mechanisms.","b":true},{"text":" Reasonable on standard textbook cases, unreliable on anything unusual, and confidently wrong on stereochemistry."}],[{"text":"Structures and diagrams.","b":true},{"text":" Text descriptions of molecular geometry are frequently muddled. Draw it. "},{"text":"Avogadro","b":true},{"text":" and "},{"text":"Jmol","b":true},{"text":" are free molecular editors; "},{"text":"ChemDraw","b":true},{"text":" is what industry names, and "},{"text":"ChemSketch","b":true},{"text":" has a free academic version."}],[{"text":"Safety information.","b":true},{"text":" Never take a hazard, incompatibility or first-aid answer from a model. Use the actual safety data sheet, which is free and legally required to exist for every reagent in your lab."}]]},{"t":"h2","id":"biology-and-the-currency-of-specifics","runs":[{"text":"Biology and the currency of specifics"}]},{"t":"p","runs":[{"text":"Biology is unusually exposed to the specificity problem: it runs on named genes, named pathways, named species, named studies and constantly-revised guidelines. A model is strong on mechanism at textbook level and unreliable on any of those particulars, especially anything revised since its training."}]},{"t":"p","runs":[{"text":"And the standing rule for anything clinical: "},{"text":"do not use it for advice about a real person, including yourself.","b":true},{"text":" Guidelines change, they differ by country, and the model has no way to know your case. Use it to understand a mechanism you are being taught. Ask a clinician about a patient."}]},{"t":"h2","id":"what-the-model-is-good-at-here","runs":[{"text":"What the model is good at here"}]},{"t":"p","runs":[{"text":"Explaining why a formula has the form it has. Building intuition for a concept before the maths. Generating practice problems of a named type. Checking your working for the "},{"text":"first","i":true},{"text":" wrong line. Explaining a paper’s methods section. Suggesting what could have caused an anomalous result in your data, as a list of hypotheses for you to test, which is a real and underused move for a discussion section, provided you evaluate the hypotheses rather than reporting them."}]}],"check":{"question":[{"text":"A student checks a generated solution and finds the units come out as kg m s⁻² where the answer should be in joules. What have they learned?"}],"options":[{"text":[{"text":"That an error exists upstream: a quantity used to the wrong power or a wrong formula."}],"correct":true,"tempting":null},{"text":[{"text":"That significant figures were applied at the wrong stage of the calculation."}],"correct":false,"tempting":[{"text":"Confuses precision with dimension; rounding never changes what physical quantity a result represents."}]},{"text":[{"text":"That the final numerical value needs converting into the correct unit before submission."}],"correct":false,"tempting":[{"text":"Treats a dimensional mismatch as a units conversion; newtons and joules differ by a length, so no conversion factor exists between them."}]},{"text":[{"text":"That the model used a different but equivalent formulation, since force times distance and energy are dimensionally related quantities in some conventions."}],"correct":false,"tempting":[{"text":"Invents a convention; force times distance is energy precisely because the dimensions differ by a length, which is what the missing factor reveals."}]}],"order":[3,0,2,1],"why":null},"prev":{"slug":"programming-and-cs","title":"Code that runs and is wrong","minutes":9},"next":{"slug":"history-and-sources","title":"History, and the quotation that was never said","minutes":8}}}