// Numbas version: exam_results_page_options
{"percentPass": 0, "duration": 0, "question_groups": [{"pickingStrategy": "all-ordered", "name": "Group", "pickQuestions": 1, "questions": [{"name": "Multiplication and division of numbers in standard index form", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Stanislav Duris", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1590/"}], "tags": ["division", "indices", "multiplication", "standard form", "standard index form", "taxonomy"], "metadata": {"description": "<p>Multiply two numbers in standard form, then divide two numbers in standard form.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Simplify,&nbsp;leaving the result in&nbsp;standard index form.</p>", "advice": "<p>We use the rules for multiplying and dividing powers.</p>\n<p style=\"padding-left: 30px;\">To <strong>multiply</strong> powers we <strong>add</strong>,&nbsp;for example&nbsp;$10^2 \\times 10^6 = 10^{(2+6)} = 10^{8}$.</p>\n<p style=\"padding-left: 30px;\">To&nbsp;<strong>divide</strong> powers we <strong>subtract</strong>, for example $10^2 \\div 10^6 = 10^{(2-6)} =&nbsp;10^{-4}$.</p>\n<p style=\"padding-left: 30px;\">&nbsp;</p>\n<h4>a)</h4>\n<p>\\[ \\begin{align} (\\var{int} \\times&nbsp;10^\\var{ran - 3}&nbsp;) \\times (\\var{int - 11}&nbsp;\\times 10^\\var{ran})&nbsp; &amp;= \\var{int} \\times (\\var{int-11}) \\times 10^{(\\var{ran - 3} + \\var{ran})} \\\\&amp;= (\\var{int*(int-11)}) \\times 10^{\\var{ran - 3 + ran}} \\end{align} \\]</p>\n<p>We want to write this number in standard form so we move decimal place one place to the left to get</p>\n<p>\\[(\\var{int*(int-11)/10}) \\times 10^{(\\var{ran - 3 + ran} + 1)} = (\\var{int*(int-11)/10}) \\times 10^{\\var{ran -&nbsp;2 + ran}} \\text{.}\\]</p>\n<h4>&nbsp;</h4>\n<h4>b)</h4>\n<p>Similarly,</p>\n<p>\\[ \\begin{align} (\\var{int*int} \\times&nbsp;10^\\var{ran -4}&nbsp;) \\div (\\var{int}&nbsp;\\times 10^\\var{ran - 2})&nbsp; &amp;= \\var{int*int} \\div \\var{int} \\times 10^{(\\var{ran - 4} - \\var{ran -2})} \\\\&amp;= \\var{int} \\times 10^{-2} \\text{.}\\end{align} \\]</p>", "rulesets": {}, "variables": {"int": {"name": "int", "group": "Ungrouped variables", "definition": "random(2..9)", "description": "", "templateType": "anything"}, "ran": {"name": "ran", "group": "Ungrouped variables", "definition": "random([6,7,8,9,10])", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["ran", "int"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p style=\"padding-left: 30px;\">$(\\var{int} \\times&nbsp;10^\\var{ran - 3}&nbsp;) \\times (\\var{int - 11}&nbsp;\\times 10^\\var{ran})&nbsp; =$&nbsp; [[0]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "answer": "{(int)*(int - 11)/10}*10^{{2*ran - 2}}", "answerSimplification": "!collectnumbers", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "musthave": {"strings": ["*10^"], "showStrings": false, "partialCredit": 0, "message": ""}, "notallowed": {"strings": ["10^3", "10^4", "10^5", "10^6", "10^7", "10^(3)", "10^(4)", "10^(5)", "10^(6)", "10^(7)", "81", "24", "28", "30"], "showStrings": false, "partialCredit": 0, "message": ""}, "valuegenerators": []}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "prompt": "<p style=\"padding-left: 30px;\">$(\\var{int*int} \\times&nbsp;10^\\var{ran -4}&nbsp;) \\div (\\var{int}&nbsp;\\times 10^\\var{ran - 2})&nbsp; =$&nbsp; [[0]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "adaptiveMarkingPenalty": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "answer": "{int}*10^(-2)", "answerSimplification": "!collectnumbers", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "musthave": {"strings": ["*10^"], "showStrings": false, "partialCredit": 0, "message": ""}, "notallowed": {"strings": ["/", "10^4", "10^(4)", "10^5", "10^(5)", "10^6", "10^(6)"], "showStrings": false, "partialCredit": 0, "message": ""}, "valuegenerators": []}], "sortAnswers": false}]}, {"name": "Addition and subtraction of numbers in standard form", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Stanislav Duris", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1590/"}], "variable_groups": [], "functions": {}, "rulesets": {}, "ungrouped_variables": ["B"], "metadata": {"description": "<p>Add two numbers in standard form, then subtract two numbers in standard form.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "advice": "<p>The easiest way to do this is to convert these numbers in standard form&nbsp;into decimals,&nbsp;do the calculation with decimal forms,&nbsp;then change them back into standard form.</p>\n<h4>a)</h4>\n<p style=\"padding-left: 30px;\">\\[\\begin{align} \\var{B[0]} \\times 10^3 + \\var{B[1]} \\times 10^4 &amp;= \\var{B[0]*10^3}&nbsp;+ \\var{B[1]*10^4} \\\\&amp;= \\var{B[0]*10^3 + B[1]*10^4} \\\\&amp;= \\var{(B[0]*10^3 + B[1]*10^4)/10^4} \\times 10^4\\end{align}\\]</p>\n<p style=\"padding-left: 30px;\">&nbsp;</p>\n<h4>b)</h4>\n<p style=\"padding-left: 30px;\">\\[\\begin{align} \\var{B[2]} \\times 10^3&nbsp;- \\var{B[2] - 1.70} \\times 10^2 &amp;= \\var{B[2]*10^3}&nbsp;- \\var{(B[2] - 1.70)*10^2} \\\\&amp;= \\var{(B[2]*10^3)&nbsp;- ((B[2] - 1.70)*10^2)} \\\\&amp;= \\var{(B[2]*10^3 - (B[2] - 1.70)*10^2)/10^3} \\times 10^3\\end{align}\\]</p>", "statement": "<p>Calculate the following and&nbsp;write the result in standard index form (for example, for&nbsp;$2.01\\times 10^5$ we would write <code>2.01*10^5</code> in the gap).</p>", "preamble": {"css": "", "js": ""}, "variables": {"B": {"templateType": "anything", "description": "", "name": "B", "group": "Ungrouped variables", "definition": "repeat(random(3..9 #0.01), 3)"}}, "parts": [{"variableReplacementStrategy": "originalfirst", "prompt": "<p style=\"padding-left: 30px;\">$\\var{B[0]} \\times 10^3 + \\var{B[1]} \\times 10^4 =$&nbsp; [[0]]</p>\n<p></p>\n<p></p>", "gaps": [{"variableReplacementStrategy": "originalfirst", "answer": "{(B[0]*10^3 + B[1]*10^4)/10^4}*10^4", "answersimplification": "!collectnumbers", "vsetrangepoints": 5, "notallowed": {"message": "", "showStrings": false, "partialCredit": 0, "strings": ["10^-4", "10^(-4)", "+", "-"]}, "checkingtype": "absdiff", "type": "jme", "showpreview": true, "checkvariablenames": false, "checkingaccuracy": 0.001, "vsetrange": [0, 1], "variableReplacements": [], "expectedvariablenames": [], "showFeedbackIcon": true, "musthave": {"message": "", "showStrings": false, "partialCredit": 0, "strings": ["*10^4"]}, "marks": 1, "showCorrectAnswer": true, "scripts": {}}], "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "type": "gapfill", "marks": 0, "showCorrectAnswer": true}, {"variableReplacementStrategy": "originalfirst", "prompt": "<p style=\"padding-left: 30px;\">$\\var{B[2]} \\times 10^3&nbsp;- \\var{B[2] - 1.70} \\times 10^2 =$&nbsp; [[0]]</p>\n<p></p>\n<p></p>\n<p></p>", "gaps": [{"variableReplacementStrategy": "originalfirst", "answer": "{(B[2]*10^3 - (B[2] - 1.70)*10^2)/10^3}*10^3", "answersimplification": "!collectnumbers", "vsetrangepoints": 5, "notallowed": {"message": "<p>+</p>\n<p></p>", "showStrings": false, "partialCredit": 0, "strings": ["*10^-3", "*10^(-3)", "+", "-"]}, "checkingtype": "absdiff", "type": "jme", "showpreview": true, "checkvariablenames": false, "checkingaccuracy": 0.001, "vsetrange": [0, 1], "variableReplacements": [], "expectedvariablenames": [], "showFeedbackIcon": true, "musthave": {"message": "", "showStrings": false, "partialCredit": 0, "strings": ["*10^3"]}, "marks": 1, "showCorrectAnswer": true, "scripts": {}}], "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "type": "gapfill", "marks": 0, "showCorrectAnswer": true}], "tags": ["addition", "Addition", "conversion", "converting", "standard form", "standard index form", "subtraction", "taxonomy"], "variablesTest": {"maxRuns": 100, "condition": ""}}]}], "feedback": {"showtotalmark": true, "allowrevealanswer": true, "showactualmark": true, "advicethreshold": 0, "showanswerstate": true, "intro": "", "feedbackmessages": []}, "metadata": {"description": "<p>Questions on adding, subtracting, multiplying and dividing numbers in standard form.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "showstudentname": true, "navigation": {"showresultspage": "oncompletion", "preventleave": true, "allowregen": true, "reverse": true, "showfrontpage": true, "onleave": {"message": "", "action": "none"}, "browse": true}, "name": "Numbers in standard form", "showQuestionGroupNames": false, "timing": {"timeout": {"message": "", "action": "none"}, "allowPause": true, "timedwarning": {"message": "", "action": "none"}}, "type": "exam", "contributors": [{"name": "Angus Rosenburgh", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2048/"}], "extensions": [], "custom_part_types": [], "resources": []}