// Numbas version: exam_results_page_options
{"name": "Simon's copy of Q7 (Calculate the estimate, actual and from these the percentage error)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"tags": [], "ungrouped_variables": ["num1", "num2", "num3", "num4", "num5", "num7", "num6", "num8", "num9", "num10", "num11", "num12", "num13", "num14", "num15", "num16", "num17", "num18", "num19", "num20", "num21", "ans11", "ans21", "ans31", "ans41", "ans51", "ans61", "ans12", "ans22", "ans32", "ans42", "ans52", "ans62", "ans13", "ans23", "ans33", "ans43", "ans53", "ans63"], "variablesTest": {"maxRuns": 100, "condition": ""}, "functions": {"hun": {"definition": "random(301..599)", "language": "jme", "type": "number", "parameters": []}, "hun1": {"definition": "random(400..600)", "language": "jme", "type": "number", "parameters": []}, "tens": {"definition": "random(35..80#0.01)", "language": "jme", "type": "number", "parameters": []}, "sin": {"definition": "random(3..8#0.01)", "language": "jme", "type": "number", "parameters": []}}, "variable_groups": [], "name": "Simon's copy of Q7 (Calculate the estimate, actual and from these the percentage error)", "statement": "<p>By rounding each number correct to one significant figure, estimate the answer to each of the problems given below, giving your final estimate to 4 d.p.</p>\n<p>Then use your calculator to correctly evaluate the exact calculation to&nbsp;4 d.p.</p>\n<p>Calculate the percentage error in using the estimate, correct to one decimal place.</p>\n<p><strong>&nbsp;</strong></p>", "variables": {"num13": {"name": "num13", "definition": "random(3.5..5.5#0.01 except num12)", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "num2": {"name": "num2", "definition": "hun1() ", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "ans63": {"name": "ans63", "definition": "(abs(ans61 - ans62)/ ans62)*100", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "num15": {"name": "num15", "definition": "hun()", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "num18": {"name": "num18", "definition": "random(201..299 except num16)", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "ans21": {"name": "ans21", "definition": "(siground(num5,1)+siground(num6,1))/siground(num7,1)", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "ans32": {"name": "ans32", "definition": "(num8*num9)/(num10)", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "ans52": {"name": "ans52", "definition": "(num15-num16)/(num17+num18)", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "num16": {"name": "num16", "definition": "random(201..299)", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "ans43": {"name": "ans43", "definition": "(abs(ans41 - ans42)/ ans42)*100", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "ans23": {"name": "ans23", "definition": "(abs(ans21 - ans22)/ ans22)*100", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "ans62": {"name": "ans62", "definition": "(num19^2*num20)/(num21)", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "num3": {"name": "num3", "definition": "precround(tens(),0)", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "ans42": {"name": "ans42", "definition": "(num11-num12)/(num13+num14)", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "num17": {"name": "num17", "definition": "random(41..59 except 50)", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "num5": {"name": "num5", "definition": "random(120..140#0.01)", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "ans41": {"name": "ans41", "definition": "(siground(num11,1)-siground(num12,1))/(siground(num13,1)+siground(num14,1))", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "ans51": {"name": "ans51", "definition": "(siground(num15,1)-siground(num16,1))/(siground(num17,1)+siground(num18,1))", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "ans12": {"name": "ans12", "definition": "(num1*num2)/(num3*num4)", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "num9": {"name": "num9", "definition": "random(55..65#0.1 except num8 except 60)", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "num6": {"name": "num6", "definition": "random(20..30#0.01)", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "num11": {"name": "num11", "definition": "precround(tens(),1)", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "num7": {"name": "num7", "definition": "tens()", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "ans31": {"name": "ans31", "definition": "(siground(num8,1)*siground(num9,1))/siground(num10,1)", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "num14": {"name": "num14", "definition": "random(11..25#0.01 except num11)", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "ans53": {"name": "ans53", "definition": "(abs(ans51 - ans52)/ ans52)*100", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "num1": {"name": "num1", "definition": "hun()", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "num8": {"name": "num8", "definition": "precround(tens(),1)", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "num4": {"name": "num4", "definition": "random(35..80 except num3)", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "num21": {"name": "num21", "definition": "random(800.1..899#0.2)", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "ans11": {"name": "ans11", "definition": "(siground(num1,1)*siground(num2,1))/(siground(num3,1)*siground(num4,1))", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "num20": {"name": "num20", "definition": "tens()", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "ans13": {"name": "ans13", "definition": "(abs(ans11 - ans12)/ ans12)*100", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "ans33": {"name": "ans33", "definition": "(abs(ans31 - ans32)/ ans32)*100", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "ans22": {"name": "ans22", "definition": "(num5+num6)/(num7)", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "num19": {"name": "num19", "definition": "sin()", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "num12": {"name": "num12", "definition": "sin()", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "ans61": {"name": "ans61", "definition": "((siground(num19,1)^2)*siground(num20,1))/siground(num21,1)", "templateType": "anything", "group": "Ungrouped variables", "description": ""}, "num10": {"name": "num10", "definition": "random(15..30#0.1 except num8)", "templateType": "anything", "group": "Ungrouped variables", "description": ""}}, "metadata": {"description": "<p>(Calculate the estimate, actual and from these the percentage error)</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "advice": "<p>When rounding off a number to one significant place, round to the left most figure of the number,&nbsp;e.g:</p>\n<p>$367 \\rightarrow 400$,&nbsp; &nbsp; &nbsp; &nbsp;$38 \\rightarrow 40$,&nbsp; &nbsp; &nbsp; &nbsp;$71 \\rightarrow 70$</p>\n<p>$3.79 \\rightarrow 4$,&nbsp; &nbsp; &nbsp; &nbsp;$65.13 \\rightarrow 70$,&nbsp; &nbsp; &nbsp; &nbsp;$0.0215 \\rightarrow 0.02$</p>\n<p>$0.00465 \\rightarrow 0.005$</p>\n<p></p>\n<p><strong>(a)</strong></p>\n<p></p>\n<p>Round each number to one significant number:</p>\n<p>$\\var{num1}&nbsp;\\rightarrow \\var{siground(num1,1)}$,&nbsp; &nbsp; &nbsp; &nbsp; $\\var{num2} \\rightarrow&nbsp;\\var{siground(num2,1)}$</p>\n<p>$\\var{num3}&nbsp;\\rightarrow \\var{siground(num3,1)}$,&nbsp; &nbsp; &nbsp; &nbsp; $\\var{num4} \\rightarrow \\var{siground(num4,1)}$</p>\n<p></p>\n<p>So for our approximation we use:&nbsp;</p>\n<p>$\\frac{\\var{siground(num1,1)}&nbsp;\\times \\var{siground(num2,1)}}{\\var{siground(num3,1)} \\times \\var{siground(num4,1)}} = \\var{precround(ans11,4)}$</p>\n<p>remembering to give our answer to 4 d.p. as requested.</p>\n<p></p>\n<p>The exact value is:</p>\n<p>$\\frac{(\\var{num1} \\times \\var{num2})}{(\\var{num3} \\times \\var{num4})} = \\var{precround(ans12,4)}$</p>\n<p></p>\n<p><strong></strong>So our percentage error:</p>\n<p>$\\frac{|\\var{precround(ans12,4)} - \\var{precround(ans11,4)}|}{\\var{precround(ans11,4)}} \\times 100 = \\var{precround(ans13,1)}$%</p>\n<p></p>\n<p><strong>(b),(c),(d)&nbsp;</strong>can be completed using a similar method</p>", "parts": [{"extendBaseMarkingAlgorithm": true, "scripts": {}, "type": "gapfill", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "variableReplacements": [], "gaps": [{"extendBaseMarkingAlgorithm": true, "correctAnswerStyle": "plain", "scripts": {}, "precisionMessage": "You have not given your answer to the correct precision.", "maxValue": "{ans11}", "allowFractions": false, "precisionType": "dp", "variableReplacementStrategy": "originalfirst", "marks": 1, "variableReplacements": [], "precision": "4", "minValue": "{ans11}", "unitTests": [], "showPrecisionHint": false, "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "type": "numberentry", "correctAnswerFraction": false, "mustBeReducedPC": 0, "showFeedbackIcon": true, "customMarkingAlgorithm": "", "precisionPartialCredit": 0, "showCorrectAnswer": true, "strictPrecision": true}, {"extendBaseMarkingAlgorithm": true, "correctAnswerStyle": "plain", "scripts": {}, "precisionMessage": "You have not given your answer to the correct precision.", "maxValue": "{ans12}", "allowFractions": false, "precisionType": "dp", "variableReplacementStrategy": "originalfirst", "marks": 1, "variableReplacements": [], "precision": "4", "minValue": "{ans12}", "unitTests": [], "showPrecisionHint": false, "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "type": "numberentry", "correctAnswerFraction": false, "mustBeReducedPC": 0, "showFeedbackIcon": true, "customMarkingAlgorithm": "", "precisionPartialCredit": 0, "showCorrectAnswer": true, "strictPrecision": true}, {"extendBaseMarkingAlgorithm": true, "correctAnswerStyle": "plain", "scripts": {}, "precisionMessage": "You have not given your answer to the correct precision.", "maxValue": "{ans13}", "allowFractions": false, "precisionType": "dp", "variableReplacementStrategy": "originalfirst", "marks": 1, "variableReplacements": [], "precision": "1", "minValue": "{ans13}", "unitTests": [], "showPrecisionHint": false, "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "type": "numberentry", "correctAnswerFraction": false, "mustBeReducedPC": 0, "showFeedbackIcon": true, "customMarkingAlgorithm": "", "precisionPartialCredit": 0, "showCorrectAnswer": true, "strictPrecision": false}], "prompt": "<p>$\\frac{\\var{num1} \\times \\var{num2}}{\\var{num3} \\times \\var{num4}}$</p>\n<p>Estimate (4dp): &nbsp; &nbsp; &nbsp;&nbsp;[[0]]</p>\n<p>Actual (4dp): &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;[[1]]</p>\n<p>% Error (1dp):&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; [[2]]%</p>", "marks": 0, "sortAnswers": false, "unitTests": [], "customMarkingAlgorithm": "", "showCorrectAnswer": true}, {"extendBaseMarkingAlgorithm": true, "scripts": {}, "type": "gapfill", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "variableReplacements": [], "gaps": [{"extendBaseMarkingAlgorithm": true, "correctAnswerStyle": "plain", "scripts": {}, "precisionMessage": "You have not given your answer to the correct precision.", "maxValue": "{ans21}", "allowFractions": false, "precisionType": "dp", "variableReplacementStrategy": "originalfirst", "marks": 1, "variableReplacements": [], "precision": "4", "minValue": "{ans21}", "unitTests": [], "showPrecisionHint": false, "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "type": "numberentry", "correctAnswerFraction": false, "mustBeReducedPC": 0, "showFeedbackIcon": true, "customMarkingAlgorithm": "", "precisionPartialCredit": 0, "showCorrectAnswer": true, "strictPrecision": true}, {"extendBaseMarkingAlgorithm": true, "correctAnswerStyle": "plain", "scripts": {}, "precisionMessage": "You have not given your answer to the correct precision.", "maxValue": "{ans22}", "allowFractions": false, "precisionType": "dp", "variableReplacementStrategy": "originalfirst", "marks": 1, "variableReplacements": [], "precision": "4", "minValue": "{ans22}", "unitTests": [], "showPrecisionHint": false, "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "type": "numberentry", "correctAnswerFraction": false, "mustBeReducedPC": 0, "showFeedbackIcon": true, "customMarkingAlgorithm": "", "precisionPartialCredit": 0, "showCorrectAnswer": true, "strictPrecision": true}, {"extendBaseMarkingAlgorithm": true, "correctAnswerStyle": "plain", "scripts": {}, "precisionMessage": "You have not given your answer to the correct precision.", "maxValue": "{ans23}", "allowFractions": false, "precisionType": "dp", "variableReplacementStrategy": "originalfirst", "marks": 1, "variableReplacements": [], "precision": "1", "minValue": "{ans23}", "unitTests": [], "showPrecisionHint": false, "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "type": "numberentry", "correctAnswerFraction": false, "mustBeReducedPC": 0, "showFeedbackIcon": true, "customMarkingAlgorithm": "", "precisionPartialCredit": 0, "showCorrectAnswer": true, "strictPrecision": false}], "prompt": "<p>$\\frac{\\var{num5}&nbsp;+ \\var{num6}}{\\var{num7}}$</p>\n<p>Estimate (4dp): &nbsp; &nbsp; &nbsp;&nbsp;[[0]]</p>\n<p>Actual (4dp): &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;[[1]]</p>\n<p>% Error (1dp):&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; [[2]]%</p>", "marks": 0, "sortAnswers": false, "unitTests": [], "customMarkingAlgorithm": "", "showCorrectAnswer": true}, {"extendBaseMarkingAlgorithm": true, "scripts": {}, "type": "gapfill", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "variableReplacements": [], "gaps": [{"extendBaseMarkingAlgorithm": true, "correctAnswerStyle": "plain", "scripts": {}, "precisionMessage": "You have not given your answer to the correct precision.", "maxValue": "{ans31}", "allowFractions": false, "precisionType": "dp", "variableReplacementStrategy": "originalfirst", "marks": 1, "variableReplacements": [], "precision": "4", "minValue": "{ans31}", "unitTests": [], "showPrecisionHint": false, "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "type": "numberentry", "correctAnswerFraction": false, "mustBeReducedPC": 0, "showFeedbackIcon": true, "customMarkingAlgorithm": "", "precisionPartialCredit": 0, "showCorrectAnswer": true, "strictPrecision": true}, {"extendBaseMarkingAlgorithm": true, "correctAnswerStyle": "plain", "scripts": {}, "precisionMessage": "You have not given your answer to the correct precision.", "maxValue": "{ans32}", "allowFractions": false, "precisionType": "dp", "variableReplacementStrategy": "originalfirst", "marks": 1, "variableReplacements": [], "precision": "4", "minValue": "{ans32}", "unitTests": [], "showPrecisionHint": false, "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "type": "numberentry", "correctAnswerFraction": false, "mustBeReducedPC": 0, "showFeedbackIcon": true, "customMarkingAlgorithm": "", "precisionPartialCredit": 0, "showCorrectAnswer": true, "strictPrecision": true}, {"extendBaseMarkingAlgorithm": true, "correctAnswerStyle": "plain", "scripts": {}, "precisionMessage": "You have not given your answer to the correct precision.", "maxValue": "{ans33}", "allowFractions": false, "precisionType": "dp", "variableReplacementStrategy": "originalfirst", "marks": 1, "variableReplacements": [], "precision": "1", "minValue": "{ans33}", "unitTests": [], "showPrecisionHint": false, "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "type": "numberentry", "correctAnswerFraction": false, "mustBeReducedPC": 0, "showFeedbackIcon": true, "customMarkingAlgorithm": "", "precisionPartialCredit": 0, "showCorrectAnswer": true, "strictPrecision": false}], "prompt": "<p>$\\frac{\\var{num8} \\times \\var{num9}}{\\var{num10}}$</p>\n<p>Estimate (4dp): &nbsp; &nbsp; &nbsp;[[0]]</p>\n<p>Actual (4dp): &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;[[1]]</p>\n<p>% Error (1dp):&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; [[2]]%</p>", "marks": 0, "sortAnswers": false, "unitTests": [], "customMarkingAlgorithm": "", "showCorrectAnswer": true}, {"extendBaseMarkingAlgorithm": true, "scripts": {}, "type": "gapfill", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "variableReplacements": [], "gaps": [{"extendBaseMarkingAlgorithm": true, "correctAnswerStyle": "plain", "scripts": {}, "precisionMessage": "You have not given your answer to the correct precision.", "maxValue": "{ans61}", "allowFractions": false, "precisionType": "dp", "variableReplacementStrategy": "originalfirst", "marks": 1, "variableReplacements": [], "precision": "4", "minValue": "{ans61}", "unitTests": [], "showPrecisionHint": false, "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "type": "numberentry", "correctAnswerFraction": false, "mustBeReducedPC": 0, "showFeedbackIcon": true, "customMarkingAlgorithm": "", "precisionPartialCredit": 0, "showCorrectAnswer": true, "strictPrecision": true}, {"extendBaseMarkingAlgorithm": true, "correctAnswerStyle": "plain", "scripts": {}, "precisionMessage": "You have not given your answer to the correct precision.", "maxValue": "{ans62}", "allowFractions": false, "precisionType": "dp", "variableReplacementStrategy": "originalfirst", "marks": 1, "variableReplacements": [], "precision": "4", "minValue": "{ans62}", "unitTests": [], "showPrecisionHint": false, "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "type": "numberentry", "correctAnswerFraction": false, "mustBeReducedPC": 0, "showFeedbackIcon": true, "customMarkingAlgorithm": "", "precisionPartialCredit": 0, "showCorrectAnswer": true, "strictPrecision": true}, {"extendBaseMarkingAlgorithm": true, "correctAnswerStyle": "plain", "scripts": {}, "precisionMessage": "You have not given your answer to the correct precision.", "maxValue": "{ans63}", "allowFractions": false, "precisionType": "dp", "variableReplacementStrategy": "originalfirst", "marks": 1, "variableReplacements": [], "precision": "1", "minValue": "{ans63}", "unitTests": [], "showPrecisionHint": false, "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "type": "numberentry", "correctAnswerFraction": false, "mustBeReducedPC": 0, "showFeedbackIcon": true, "customMarkingAlgorithm": "", "precisionPartialCredit": 0, "showCorrectAnswer": true, "strictPrecision": false}], "prompt": "<p>$\\frac{\\var{num19}^2 \\times \\var{num20}}{\\var{num21}}$</p>\n<p>Estimate (4dp): &nbsp; &nbsp; &nbsp;[[0]]</p>\n<p>Actual (4dp): &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;[[1]]</p>\n<p>% Error (1dp):&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; [[2]]%</p>", "marks": 0, "sortAnswers": false, "unitTests": [], "customMarkingAlgorithm": "", "showCorrectAnswer": true}], "preamble": {"js": "", "css": ""}, "rulesets": {}, "extensions": [], "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/"}]}