// Numbas version: finer_feedback_settings
{"name": "Simon's copy of Q2 Convert from one measurement scale to another", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"extensions": [], "statement": "<p>Convert the following.</p>\n<p>Do not answer in&nbsp;scientific notation.</p>", "preamble": {"css": "", "js": ""}, "tags": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "ungrouped_variables": ["num", "ans1", "ans2", "ans3", "ans4", "ans5", "ans6", "num2", "ans31", "ans32", "ans33", "ans34", "ans35"], "rulesets": {}, "parts": [{"prompt": "<p>i) $\\var{num2[0]}$ $mm^2$ to $cm^2$.&nbsp;</p>\n<p>[[0]]&nbsp;$cm^2$</p>\n<p>ii) $\\var{num2[1]}$ $mm^3$ to $cm^3$.&nbsp;</p>\n<p>[[1]]&nbsp;$cm^3$</p>\n<p>iii) $\\var{num2[2]}$ $cm^2$ to $m^2$.&nbsp;</p>\n<p>[[2]]&nbsp;$m^2$</p>\n<p>iv) $\\var{num2[3]}$ $cm^3$ to $m^3$.&nbsp;</p>\n<p>[[3]]&nbsp;$m^3$</p>\n<p>v) $\\var{num2[4]}$ $mm^3$ to $m^3$.</p>\n<p>[[4]]&nbsp;$m^3$</p>", "scripts": {}, "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "unitTests": [], "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "showCorrectAnswer": true, "gaps": [{"minValue": "{ans31}", "correctAnswerFraction": false, "mustBeReduced": false, "mustBeReducedPC": 0, "variableReplacements": [], "precisionMessage": "You have not given your answer to the correct precision.", "correctAnswerStyle": "plain", "precisionType": "dp", "type": "numberentry", "scripts": {}, "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "unitTests": [], "showPrecisionHint": false, "extendBaseMarkingAlgorithm": true, "maxValue": "{ans31}", "showCorrectAnswer": true, "notationStyles": ["plain", "en", "si-en"], "precisionPartialCredit": 0, "precision": "7", "marks": 1, "allowFractions": false, "strictPrecision": false, "showFeedbackIcon": true}, {"minValue": "{ans32}", "correctAnswerFraction": false, "mustBeReduced": false, "mustBeReducedPC": 0, "variableReplacements": [], "precisionMessage": "You have not given your answer to the correct precision.", "correctAnswerStyle": "plain", "precisionType": "dp", "type": "numberentry", "scripts": {}, "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "unitTests": [], "showPrecisionHint": false, "extendBaseMarkingAlgorithm": true, "maxValue": "{ans32}", "showCorrectAnswer": true, "notationStyles": ["plain", "en", "si-en"], "precisionPartialCredit": 0, "precision": "3", "marks": 1, "allowFractions": false, "strictPrecision": false, "showFeedbackIcon": true}, {"minValue": "{ans33}", "correctAnswerFraction": false, "mustBeReduced": false, "mustBeReducedPC": 0, "variableReplacements": [], "precisionMessage": "You have not given your answer to the correct precision.", "correctAnswerStyle": "plain", "precisionType": "dp", "type": "numberentry", "scripts": {}, "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "unitTests": [], "showPrecisionHint": false, "extendBaseMarkingAlgorithm": true, "maxValue": "{ans33}", "showCorrectAnswer": true, "notationStyles": ["plain", "en", "si-en"], "precisionPartialCredit": 0, "precision": "4", "marks": 1, "allowFractions": false, "strictPrecision": false, "showFeedbackIcon": true}, {"minValue": "{ans34}", "correctAnswerFraction": false, "mustBeReduced": false, "mustBeReducedPC": 0, "variableReplacements": [], "precisionMessage": "You have not given your answer to the correct precision.", "correctAnswerStyle": "plain", "precisionType": "dp", "type": "numberentry", "scripts": {}, "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "unitTests": [], "showPrecisionHint": false, "extendBaseMarkingAlgorithm": true, "maxValue": "{ans34}", "showCorrectAnswer": true, "notationStyles": ["plain", "en", "si-en"], "precisionPartialCredit": 0, "precision": "6", "marks": 1, "allowFractions": false, "strictPrecision": false, "showFeedbackIcon": true}, {"minValue": "{ans35}", "correctAnswerFraction": false, "mustBeReduced": false, "mustBeReducedPC": 0, "variableReplacements": [], "precisionMessage": "You have not given your answer to the correct precision.", "correctAnswerStyle": "plain", "precisionType": "dp", "type": "numberentry", "scripts": {}, "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "unitTests": [], "showPrecisionHint": false, "extendBaseMarkingAlgorithm": true, "maxValue": "{ans35}", "showCorrectAnswer": true, "notationStyles": ["plain", "en", "si-en"], "precisionPartialCredit": 0, "precision": "10", "marks": 1, "allowFractions": false, "strictPrecision": false, "showFeedbackIcon": true}], "showFeedbackIcon": true, "sortAnswers": false, "marks": 0, "type": "gapfill"}, {"prompt": "<p>i) $\\var{num[0]}$ square metres ($m^3$) to litres.&nbsp;</p>\n<p>[[0]]&nbsp;litres</p>\n<p>ii) $\\var{num[1]}$ $mm^3$ to litres.&nbsp;</p>\n<p>[[1]]&nbsp;litres</p>\n<p>iii) $\\var{num[2]}$ $cm^3$ to litres.&nbsp;</p>\n<p>[[2]]&nbsp;litres</p>\n<p>iv) $\\var{num[3]}$ $litres$ to $cm^3$.&nbsp;</p>\n<p>[[3]]&nbsp;$cm^3$</p>\n<p>v) $\\var{num[4]}$ $litres$ to $m^3$.&nbsp;</p>\n<p>[[4]]&nbsp;$m^3$</p>\n<p>vi)&nbsp;$\\var{num[5]}$ $litres$ to $mm^3$.&nbsp;</p>\n<p>[[5]]&nbsp;$mm^3$</p>", "scripts": {}, "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "unitTests": [], "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "showCorrectAnswer": true, "gaps": [{"scripts": {}, "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "mustBeReduced": false, "unitTests": [], "extendBaseMarkingAlgorithm": true, "correctAnswerStyle": "plain", "variableReplacements": [], "maxValue": "{ans1}", "showCorrectAnswer": true, "notationStyles": ["plain", "en", "si-en"], "showFeedbackIcon": true, "mustBeReducedPC": 0, "correctAnswerFraction": false, "marks": 1, "type": "numberentry", "minValue": "{ans1}", "allowFractions": false}, {"minValue": "{ans2}", "correctAnswerFraction": false, "mustBeReduced": false, "mustBeReducedPC": 0, "variableReplacements": [], "precisionMessage": "You have not given your answer to the correct precision.", "correctAnswerStyle": "plain", "precisionType": "dp", "type": "numberentry", "scripts": {}, "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "unitTests": [], "showPrecisionHint": false, "extendBaseMarkingAlgorithm": true, "maxValue": "{ans2}", "showCorrectAnswer": true, "notationStyles": ["plain", "en", "si-en"], "precisionPartialCredit": 0, "precision": "4", "marks": 1, "allowFractions": false, "strictPrecision": false, "showFeedbackIcon": true}, {"minValue": "{ans3}", "correctAnswerFraction": false, "mustBeReduced": false, "mustBeReducedPC": 0, "variableReplacements": [], "precisionMessage": "You have not given your answer to the correct precision.", "correctAnswerStyle": "plain", "precisionType": "dp", "type": "numberentry", "scripts": {}, "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "unitTests": [], "showPrecisionHint": false, "extendBaseMarkingAlgorithm": true, "maxValue": "{ans3}", "showCorrectAnswer": true, "notationStyles": ["plain", "en", "si-en"], "precisionPartialCredit": 0, "precision": "1", "marks": 1, "allowFractions": false, "strictPrecision": false, "showFeedbackIcon": true}, {"scripts": {}, "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "mustBeReduced": false, "unitTests": [], "extendBaseMarkingAlgorithm": true, "correctAnswerStyle": "plain", "variableReplacements": [], "maxValue": "{ans4}", "showCorrectAnswer": true, "notationStyles": ["plain", "en", "si-en"], "showFeedbackIcon": true, "mustBeReducedPC": 0, "correctAnswerFraction": false, "marks": 1, "type": "numberentry", "minValue": "{ans4}", "allowFractions": false}, {"minValue": "{ans5}", "correctAnswerFraction": false, "mustBeReduced": false, "mustBeReducedPC": 0, "variableReplacements": [], "precisionMessage": "You have not given your answer to the correct precision.", "correctAnswerStyle": "plain", "precisionType": "dp", "type": "numberentry", "scripts": {}, "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "unitTests": [], "showPrecisionHint": false, "extendBaseMarkingAlgorithm": true, "maxValue": "{ans5}", "showCorrectAnswer": true, "notationStyles": ["plain", "en", "si-en"], "precisionPartialCredit": 0, "precision": "1", "marks": 1, "allowFractions": false, "strictPrecision": false, "showFeedbackIcon": true}, {"scripts": {}, "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "mustBeReduced": false, "unitTests": [], "extendBaseMarkingAlgorithm": true, "correctAnswerStyle": "plain", "variableReplacements": [], "maxValue": "{ans6}", "showCorrectAnswer": true, "notationStyles": ["plain", "en", "si-en"], "showFeedbackIcon": true, "mustBeReducedPC": 0, "correctAnswerFraction": false, "marks": 1, "type": "numberentry", "minValue": "{ans6}", "allowFractions": false}], "showFeedbackIcon": true, "sortAnswers": false, "marks": 0, "type": "gapfill"}], "advice": "<p>1m = 100cm and 1cm = 10mm, so 1m = 1000mm. When we are converting to larger units we must divide. Therefore:</p>\n<p>To convert from cm$^2$ to m$^2$ we divide by $100^2$</p>\n<p>To convert from mm$^2$ to m$^2$ we divide by $1000^2$</p>\n<p>To convert from mm$^2$ to cm$^2$ we divide by $10^2$</p>\n<p>To convert from cm$^3$ to m$^3$ we divide by $100^3$</p>\n<p>To convert from mm$^3$ to m$^3$ we divide by $1000^3$</p>\n<p>To convert from mm$^3$ to cm$^3$ we divide by $10^3$</p>\n<p></p>\n<p>1 litre is 1000cm$^3$. Therefore:</p>\n<p>To convert from litres we can multiply by 1000 at the start, then convert from&nbsp;cm$^3$.</p>\n<p>To convert to litres we can convert to cm$^3$, then divide by 1000 at the end.</p>\n<p></p>\n<p>Part 1</p>\n<p>i) $\\frac{\\var{num2[0]}}{10^2} = \\var{ans31}$</p>\n<p>ii) $\\frac{\\var{num2[1]}}{10^3} =&nbsp;\\var{ans32}$</p>\n<p>iii) $\\frac{\\var{num2[2]}}{100^2} =&nbsp;\\var{ans33}$</p>\n<p>iv) $\\frac{\\var{num2[3]}}{100^3}&nbsp;= \\var{ans34}$</p>\n<p>v) $\\frac{\\var{num2[4]}}{1000^3}&nbsp;= &nbsp;\\var{ans35}$</p>\n<p>Part 2</p>\n<p>i) $\\frac{\\var{num[0]} \\times 100^3}{1000} = \\var{ans1}$</p>\n<p>ii) $\\frac{\\var{num[1]}}{10^3\\times1000} = \\var{ans2}$</p>\n<p>iii) $\\frac{\\var{num[2]}}{1000} = \\var{ans3}$</p>\n<p>iv) $\\var{num[3]} \\times 1000 = \\var{ans4}$</p>\n<p>v) $\\frac{\\var{num[4]}\\times 1000}{100^3} = \\var{ans5}$</p>\n<p>vi) $\\var{num[5]}\\times 1000 \\times&nbsp; 10^3 = \\var{ans6}$</p>", "functions": {}, "metadata": {"description": "<p>Convert from one measurement scale to another</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "variables": {"ans31": {"name": "ans31", "group": "Ungrouped variables", "definition": "num2[0]/100", "templateType": "anything", "description": ""}, "ans32": {"name": "ans32", "group": "Ungrouped variables", "definition": "num2[1]/1000", "templateType": "anything", "description": ""}, "ans35": {"name": "ans35", "group": "Ungrouped variables", "definition": "num2[4]/1000000000", "templateType": "anything", "description": ""}, "ans1": {"name": "ans1", "group": "Ungrouped variables", "definition": "num[0]*1000", "templateType": "anything", "description": ""}, "ans2": {"name": "ans2", "group": "Ungrouped variables", "definition": "num[1]/1000000", "templateType": "anything", "description": ""}, "ans6": {"name": "ans6", "group": "Ungrouped variables", "definition": "num[5]*1000000", "templateType": "anything", "description": ""}, "num": {"name": "num", "group": "Ungrouped variables", "definition": "shuffle(2000..60000#100)[0..6]", "templateType": "anything", "description": ""}, "num2": {"name": "num2", "group": "Ungrouped variables", "definition": "shuffle(600..2200#5)[0..5]", "templateType": "anything", "description": ""}, "ans4": {"name": "ans4", "group": "Ungrouped variables", "definition": " num[3]*1000", "templateType": "anything", "description": ""}, "ans3": {"name": "ans3", "group": "Ungrouped variables", "definition": "num[2]/1000", "templateType": "anything", "description": ""}, "ans5": {"name": "ans5", "group": "Ungrouped variables", "definition": "num[4]/1000", "templateType": "anything", "description": ""}, "ans34": {"name": "ans34", "group": "Ungrouped variables", "definition": "num2[3]/1000000", "templateType": "anything", "description": ""}, "ans33": {"name": "ans33", "group": "Ungrouped variables", "definition": "num2[2]/10000", "templateType": "anything", "description": ""}}, "name": "Simon's copy of Q2 Convert from one measurement scale to another", "variable_groups": [], "type": "question", "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}]}], "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}