// Numbas version: finer_feedback_settings
{"name": "32.d Adding/Subtracting standard form", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "32.d Adding/Subtracting standard form", "tags": ["converting", "scientific notation", "standard form"], "metadata": {"description": "<p>Convert numbers between 0 and 1 intro standard form/scientific notation.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Calculate the following expression and write the answer in standard form.</p>", "advice": "<p>{advice}</p>\n<p><a href=\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Standard\"><span style=\"font-weight: 400;\">Use this link to find some resources which will help you revise this topic.</span></a></p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"PowAns": {"name": "PowAns", "group": "Ungrouped variables", "definition": "if(ChangePower, max(Pow1,Pow2)+1, max(Pow1,Pow2))", "description": "", "templateType": "anything", "can_override": false}, "NumAns": {"name": "NumAns", "group": "Ungrouped variables", "definition": "if(ChangePower, AddNums/10, AddNums)", "description": "", "templateType": "anything", "can_override": false}, "Num1": {"name": "Num1", "group": "Ungrouped variables", "definition": "random(1..9#0.1)", "description": "", "templateType": "anything", "can_override": false}, "Num2": {"name": "Num2", "group": "Ungrouped variables", "definition": "random(1..9#0.1)*random(-1,1)", "description": "", "templateType": "anything", "can_override": false}, "Pow1": {"name": "Pow1", "group": "Ungrouped variables", "definition": "random(-12..12)", "description": "", "templateType": "anything", "can_override": false}, "Pow2": {"name": "Pow2", "group": "Ungrouped variables", "definition": "Pow1+PowDiff", "description": "", "templateType": "anything", "can_override": false}, "ChangePower": {"name": "ChangePower", "group": "Ungrouped variables", "definition": "AddNums>=10", "description": "", "templateType": "anything", "can_override": false}, "Advice": {"name": "Advice", "group": "Advice", "definition": "if(PowDiff=0, AdviceSamePow,if(IsPow1Bigger, AdviceNum1Bigger, AdviceNum2Bigger))+if(ChangePower, AdviceChangePower, AdviceNoChange)", "description": "", "templateType": "anything", "can_override": false}, "AdviceChangePower": {"name": "AdviceChangePower", "group": "Advice", "definition": "\"<p>This is not in standard form, we need to divide $\\\\var{AddNums}$ by $10$ and increase the power by $1$ to get a final answer of</p>\\n<p>\\\\[\\\\var{NumAns}\\\\times 10^\\\\var{PowAns}.\\\\]</p>\"", "description": "", "templateType": "long string", "can_override": false}, "AdviceNoChange": {"name": "AdviceNoChange", "group": "Advice", "definition": "\"<p>Since this is already in standard form we are done.</p>\"", "description": "", "templateType": "long string", "can_override": false}, "PowDiff": {"name": "PowDiff", "group": "Ungrouped variables", "definition": "random(-2..2)", "description": "", "templateType": "anything", "can_override": false}, "IsPow1Bigger": {"name": "IsPow1Bigger", "group": "Ungrouped variables", "definition": "PowDiff<0", "description": "", "templateType": "anything", "can_override": false}, "AddNums": {"name": "AddNums", "group": "Ungrouped variables", "definition": "if(IsPow1Bigger, Num1+Num2*10^PowDiff, Num1*10^-PowDiff+Num2)", "description": "", "templateType": "anything", "can_override": false}, "AdviceNum1Bigger": {"name": "AdviceNum1Bigger", "group": "Advice", "definition": "\"<p>To add or subtract numbers in standard form we need both of the powers to be the same. We will write both numbers to the power&nbsp;of $\\\\var{Pow1}$. This gives us<br />\\\\[\\\\simplify[basic]{{Num1}*10^{Pow1}+{Num2}}\\\\times 10^\\\\var{Pow2}\\\\]</p>\\n<p>\\\\[=\\\\simplify[basic]{{Num1}*10^{Pow1}+{Num2}}\\\\times10^\\\\var{PowDiff}\\\\times 10^\\\\var{Pow2-PowDiff}\\\\]</p>\\n<p>\\\\[=\\\\simplify[basic]{{Num1}*10^{Pow1}+{Num2*10^PowDiff}}\\\\times 10^\\\\var{Pow2-PowDiff}.\\\\]</p>\\n<p>Since both numbers have the same power we can now evaluate them as usual to get</p>\\n<p>\\\\[\\\\var{AddNums}\\\\times 10^\\\\var{Pow1}.\\\\]</p>\"", "description": "", "templateType": "long string", "can_override": false}, "AdviceNum2Bigger": {"name": "AdviceNum2Bigger", "group": "Advice", "definition": "\"<p>To add or subtract numbers in standard form we need both of the powers to be the same. We will write both numbers to the power of $\\\\var{Pow2}$. This gives us<br />\\\\[\\\\simplify[basic]{{Num1}*10^{Pow1}+{Num2}}\\\\times 10^\\\\var{Pow2}\\\\]</p>\\n<p>\\\\[=\\\\var{Num1}\\\\times10^\\\\var{-PowDiff}\\\\times \\\\simplify[basic]{10^{Pow1+PowDiff}+{Num2}}\\\\times 10^\\\\var{Pow2}\\\\]</p>\\n<p>\\\\[=\\\\var{Num1*10^-PowDiff}\\\\times \\\\simplify[basic]{10^{Pow1+PowDiff}+{Num2}}\\\\times 10^\\\\var{Pow2}.\\\\]</p>\\n<p>Since both numbers have the same power we can now evaluate them as usual to get</p>\\n<p>\\\\[\\\\var{AddNums}\\\\times 10^\\\\var{Pow2}.\\\\]</p>\"", "description": "", "templateType": "long string", "can_override": false}, "AdviceSamePow": {"name": "AdviceSamePow", "group": "Advice", "definition": "\"<p>To add or subtract numbers in standard form we need both of the powers to be the same. Since both numbers have a power of $\\\\var{Pow1}$ we can simply evaluate them as usual to get<br />\\\\[\\\\simplify[basic]{{Num1}*10^{Pow1}+{Num2}}\\\\times 10^\\\\var{Pow2}=\\\\var{AddNums}\\\\times 10^\\\\var{Pow1}.\\\\]</p>\"", "description": "", "templateType": "long string", "can_override": false}}, "variablesTest": {"condition": "AddNums>=1", "maxRuns": 100}, "ungrouped_variables": ["NumAns", "PowAns", "Num1", "Num2", "AddNums", "Pow1", "PowDiff", "Pow2", "IsPow1Bigger", "ChangePower"], "variable_groups": [{"name": "Advice", "variables": ["Advice", "AdviceChangePower", "AdviceNoChange", "AdviceNum1Bigger", "AdviceNum2Bigger", "AdviceSamePow"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\simplify[basic]{{Num1}*10^{Pow1}+{Num2}}\\times 10^\\var{Pow2}=$ [[0]]$\\times 10$&nbsp;<sup>[[1]]&nbsp;</sup>.</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{NumAns}", "maxValue": "{NumAns}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{PowAns}", "maxValue": "{PowAns}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"name": "Ruth Hand", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3228/"}, {"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}, {"name": "Will Morgan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21933/"}], "resources": []}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"name": "Ruth Hand", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3228/"}, {"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}, {"name": "Will Morgan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21933/"}]}