// Numbas version: finer_feedback_settings
{"name": "32.b Division in standard form", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "32.b Division in 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, Pow1-Pow2-1, Pow1-Pow2)", "description": "", "templateType": "anything", "can_override": false}, "NumAns": {"name": "NumAns", "group": "Ungrouped variables", "definition": "random(1..9)", "description": "", "templateType": "anything", "can_override": false}, "Num1": {"name": "Num1", "group": "Ungrouped variables", "definition": "if(DivdNum>=10, DivdNum*0.1, DivdNum)", "description": "", "templateType": "anything", "can_override": false}, "Num2": {"name": "Num2", "group": "Ungrouped variables", "definition": "random(1..9)", "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": "random(-12..12)", "description": "", "templateType": "anything", "can_override": false}, "ChangePower": {"name": "ChangePower", "group": "Ungrouped variables", "definition": "DivdNum>=10", "description": "", "templateType": "anything", "can_override": false}, "Advice": {"name": "Advice", "group": "Ungrouped variables", "definition": "if(ChangePower, AdviceChangePower, AdviceNoChange)", "description": "", "templateType": "anything", "can_override": false}, "AdviceChangePower": {"name": "AdviceChangePower", "group": "Ungrouped variables", "definition": "\"<p>It is easiest to think of</p>\\n<p>\\\\[\\\\left(\\\\var{Num1}\\\\times 10^\\\\var{Pow1}\\\\right)\\\\div\\\\left(\\\\var{Num2}\\\\times 10^\\\\var{Pow2}\\\\right)\\\\]</p>\\n<p>as the fraction</p>\\n<p>\\\\[\\\\frac{\\\\var{Num1}\\\\times 10^\\\\var{Pow1}}{\\\\var{Num2}\\\\times 10^\\\\var{Pow2}}\\\\]</p>\\n<p>at which point there are different ways to cancel down to one number in standard form. One option is to convert both numbers out of standard form but this can often be very messy. Alternatively we can simply divide $\\\\var{Num1}$ by $\\\\var{Num2}$ and $10^\\\\var{Pow1}$ by $10^\\\\var{Pow2}$ which gives us</p>\\n<p>\\\\[\\\\frac{\\\\var{Num1}\\\\times 10^\\\\var{Pow1}}{\\\\var{Num2}\\\\times 10^\\\\var{Pow2}}=\\\\var{Num1/Num2}\\\\times 10^\\\\var{Pow1-Pow2}.\\\\]</p>\\n<p>Since this is not in standard form we need to decrease the power by $1$ and multiply the number in front by $10$ to get a final answer of&nbsp;</p>\\n<p>\\\\[\\\\var{Num1/Num2*10}\\\\times 10^\\\\var{Pow1-Pow2-1}.\\\\]</p>\\n<p></p>\\n<p>Another option if you are not comfortable with dividing $\\\\var{Num1}$ by $\\\\var{Num2}$ is to multiply $\\\\var{Num1}$ by $10$ and decrease the power $\\\\var{Pow1}$ by $1$. This makes the division slightly easier as we get</p>\\n<p>\\\\[\\\\frac{\\\\var{Num1}\\\\times 10^\\\\var{Pow1}}{\\\\var{Num2}\\\\times 10^\\\\var{Pow2}}=\\\\frac{\\\\var{Num1*10}\\\\times 10^\\\\var{Pow1-1}}{\\\\var{Num2}\\\\times 10^\\\\var{Pow2}}=\\\\var{Num1/Num2*10}\\\\times10^\\\\var{Pow1-Pow2-1}.\\\\]</p>\\n<p>This is already in standard form so we are done.</p>\"", "description": "", "templateType": "long string", "can_override": false}, "AdviceNoChange": {"name": "AdviceNoChange", "group": "Ungrouped variables", "definition": "\"<p>It is easiest to think of</p>\\n<p>\\\\[\\\\left(\\\\var{Num1}\\\\times 10^\\\\var{Pow1}\\\\right)\\\\div\\\\left(\\\\var{Num2}\\\\times 10^\\\\var{Pow2}\\\\right)\\\\]</p>\\n<p>as the fraction</p>\\n<p>\\\\[\\\\frac{\\\\var{Num1}\\\\times 10^\\\\var{Pow1}}{\\\\var{Num2}\\\\times 10^\\\\var{Pow2}}\\\\]</p>\\n<p>and then we can cancel the terms which are easiest to divide. In this case it is easiest to divide $\\\\var{Num1}$ by $\\\\var{Num2}$ and $10^\\\\var{Pow1}$ by $10^\\\\var{Pow2}$ which gives us</p>\\n<p>\\\\[\\\\frac{\\\\var{Num1}\\\\times 10^\\\\var{Pow1}}{\\\\var{Num2}\\\\times 10^\\\\var{Pow2}}=\\\\var{Num1/Num2}\\\\times 10^\\\\var{Pow1-Pow2}.\\\\]</p>\\n<p>Since this is already in standard form then we are done.</p>\"", "description": "", "templateType": "long string", "can_override": false}, "DivdNum": {"name": "DivdNum", "group": "Ungrouped variables", "definition": "NumAns*Num2", "description": "<p>Number to divide by Num2 - not written in standard form.</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["NumAns", "PowAns", "Num1", "DivdNum", "Num2", "Pow1", "Pow2", "ChangePower", "Advice", "AdviceChangePower", "AdviceNoChange"], "variable_groups": [], "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>$\\left(\\var{Num1}\\times 10^\\var{Pow1}\\right)\\div\\left(\\var{Num2}\\times 10^\\var{Pow2}\\right)=$ [[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/"}]}