// Numbas version: exam_results_page_options
{"name": "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": [{"functions": {"tens": {"definition": "random(35..80#0.01)", "type": "number", "language": "jme", "parameters": []}, "hun": {"definition": "random(301..599)", "type": "number", "language": "jme", "parameters": []}, "sin": {"definition": "random(3..8#0.01)", "type": "number", "language": "jme", "parameters": []}, "hun1": {"definition": "random(400..600)", "type": "number", "language": "jme", "parameters": []}}, "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"], "name": "Q7 (Calculate the estimate, actual and from these the percentage error)", "tags": ["rebelmaths"], "preamble": {"css": "", "js": ""}, "advice": "<p>When rounding off a number to one significant place, round to the left most figure of the number, like below;</p>\n<p>$367 = 400$</p>\n<p>$38 = 40$</p>\n<p>$71 = 70$</p>\n<p>$3.79 = 4$</p>\n<p>$65.13 = 70$</p>\n<p>$215 = 200$</p>\n<p></p>\n<p><em>Part 1:</em></p>\n<p>Estimate value with each number rounded to one significant place:</p>\n<p>$\\frac{(\\var{num1}&nbsp;\\times \\var{num2})}{(\\var{num3} \\times \\var{num4})}$&nbsp;</p>\n<p>Round numbers to one significant number:</p>\n<p>$\\var{num1} = ${siground(num1,1)}</p>\n<p>$\\var{num2} = ${siground(num2,1)}</p>\n<p>$\\var{num3} = ${siground(num3,1)}</p>\n<p>$\\var{num4} = ${siground(num4,1)}</p>\n<p>Answer:</p>\n<p>$= \\var{ans11}$</p>\n<p></p>\n<p><em>Part 2:</em></p>\n<p>Actual value:</p>\n<p>$\\frac{(\\var{num1} \\times \\var{num2})}{(\\var{num3} \\times \\var{num4})} = \\var{ans12}$</p>\n<p></p>\n<p><em>Part 3:</em></p>\n<p>Percentage error:</p>\n<p>$abs(\\frac{\\var{ans12} - \\var{ans11}}{\\var{ans11}}) \\times 100 = \\var{ans13}$%</p>", "rulesets": {}, "parts": [{"prompt": "<p>$\\frac{\\var{num1} \\times \\var{num2}}{\\var{num3} \\times \\var{num4}}$</p>\n<p>Estimate: &nbsp; &nbsp; &nbsp;&nbsp;[[0]]</p>\n<p>Actual: &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;[[1]]</p>\n<p>% Error:&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; [[2]]%</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{ans11}", "minValue": "{ans11}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{ans12}", "minValue": "{ans12}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "integerPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{ans13}+1", "strictPrecision": false, "minValue": "{ans13}-1", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "1", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\frac{\\var{num5}&nbsp;+ \\var{num6}}{\\var{num7}}$</p>\n<p>Estimate: &nbsp; &nbsp; &nbsp;&nbsp;[[0]]</p>\n<p>Actual: &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;[[1]]</p>\n<p>% Error:&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; [[2]]%</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{ans21}", "minValue": "{ans21}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{ans22}", "minValue": "{ans22}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans23}+1", "strictPrecision": false, "minValue": "{ans23}-1", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "1", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\frac{\\var{num8} \\times \\var{num9}}{\\var{num10}}$</p>\n<p>Estimate: &nbsp; &nbsp; &nbsp;[[0]]</p>\n<p>Actual: &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;[[1]]</p>\n<p>% Error:&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; [[2]]%</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{ans31}", "minValue": "{ans31}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "{ans32}", "minValue": "{ans32}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans33}+1", "strictPrecision": false, "minValue": "{ans33}-1", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "1", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\frac{\\var{num11}&nbsp;- \\var{num12}}{\\var{num13}&nbsp;+ \\var{num14}}$</p>\n<p>Estimate: &nbsp; &nbsp; &nbsp;[[0]]</p>\n<p>Actual: &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;[[1]]</p>\n<p>% Error:&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; [[2]]%</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{ans41}", "minValue": "{ans41}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{ans42}", "minValue": "{ans42}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans43}+1", "strictPrecision": false, "minValue": "{ans43}-1", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "1", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\frac{\\var{num15}&nbsp;- \\var{num16}}{\\var{num17}&nbsp;+ \\var{num18}}$</p>\n<p>Estimate: &nbsp; &nbsp; &nbsp;[[0]]</p>\n<p>Actual: &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;[[1]]</p>\n<p>% Error:&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; [[2]]%</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{ans51}", "minValue": "{ans51}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{ans52}", "minValue": "{ans52}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans53}+1", "strictPrecision": false, "minValue": "{ans53}-1", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "1", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>$\\frac{\\var{num19}^2 \\times \\var{num20}}{\\var{num21}}$</p>\n<p>Estimate: &nbsp; &nbsp; &nbsp;[[0]]</p>\n<p>Actual: &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;[[1]]</p>\n<p>% Error:&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; [[2]]%</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{ans61}", "minValue": "{ans61}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{ans62}", "minValue": "{ans62}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "{ans63}+1", "strictPrecision": false, "minValue": "{ans63}-1", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "1", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "extensions": [], "statement": "<p>By rounding each number correct to one significant figure, estimate the answer to each of the problems given below. Then use your calculator to accurately evaluate each of them.</p>\n<p>Calculate the percentage error in using the estimate, correct to one decimal place.</p>\n<p><strong>&nbsp;</strong></p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"num4": {"definition": "random(35..80 except num3)", "templateType": "anything", "group": "Ungrouped variables", "name": "num4", "description": ""}, "num5": {"definition": "random(120..140#0.01)", "templateType": "anything", "group": "Ungrouped variables", "name": "num5", "description": ""}, "num6": {"definition": "random(20..30#0.01)", "templateType": "anything", "group": "Ungrouped variables", "name": "num6", "description": ""}, "num7": {"definition": "tens()", "templateType": "anything", "group": "Ungrouped variables", "name": "num7", "description": ""}, "num1": {"definition": "hun()", "templateType": "anything", "group": "Ungrouped variables", "name": "num1", "description": ""}, "num2": {"definition": "hun1() ", "templateType": "anything", "group": "Ungrouped variables", "name": "num2", "description": ""}, "num3": {"definition": "precround(tens(),0)", "templateType": "anything", "group": "Ungrouped variables", "name": "num3", "description": ""}, "num8": {"definition": "precround(tens(),1)", "templateType": "anything", "group": "Ungrouped variables", "name": "num8", "description": ""}, "num9": {"definition": "random(55..65#0.1 except num8 except 60)", "templateType": "anything", "group": "Ungrouped variables", "name": "num9", "description": ""}, "ans23": {"definition": "(abs(ans21 - ans22)/ ans22)*100", "templateType": "anything", "group": "Ungrouped variables", "name": "ans23", "description": ""}, "ans22": {"definition": "(num5+num6)/(num7)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans22", "description": ""}, "ans21": {"definition": "(siground(num5,1)+siground(num6,1))/siground(num7,1)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans21", "description": ""}, "ans63": {"definition": "(abs(ans61 - ans62)/ ans62)*100", "templateType": "anything", "group": "Ungrouped variables", "name": "ans63", "description": ""}, "ans62": {"definition": "(num19^2*num20)/(num21)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans62", "description": ""}, "ans61": {"definition": "((siground(num19,1)^2)*siground(num20,1))/siground(num21,1)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans61", "description": ""}, "ans41": {"definition": "(siground(num11,1)-siground(num12,1))/(siground(num13,1)+siground(num14,1))", "templateType": "anything", "group": "Ungrouped variables", "name": "ans41", "description": ""}, "ans43": {"definition": "(abs(ans41 - ans42)/ ans42)*100", "templateType": "anything", "group": "Ungrouped variables", "name": "ans43", "description": ""}, "ans42": {"definition": "(num11-num12)/(num13+num14)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans42", "description": ""}, "num21": {"definition": "random(800.1..899#0.2)", "templateType": "anything", "group": "Ungrouped variables", "name": "num21", "description": ""}, "num20": {"definition": "tens()", "templateType": "anything", "group": "Ungrouped variables", "name": "num20", "description": ""}, "ans12": {"definition": "(num1*num2)/(num3*num4)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans12", "description": ""}, "ans13": {"definition": "(abs(ans11 - ans12)/ ans12)*100", "templateType": "anything", "group": "Ungrouped variables", "name": "ans13", "description": ""}, "ans11": {"definition": "(siground(num1,1)*siground(num2,1))/(siground(num3,1)*siground(num4,1))", "templateType": "anything", "group": "Ungrouped variables", "name": "ans11", "description": ""}, "ans31": {"definition": "(siground(num8,1)*siground(num9,1))/siground(num10,1)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans31", "description": ""}, "ans32": {"definition": "(num8*num9)/(num10)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans32", "description": ""}, "ans33": {"definition": "(abs(ans31 - ans32)/ ans32)*100", "templateType": "anything", "group": "Ungrouped variables", "name": "ans33", "description": ""}, "ans52": {"definition": "(num15-num16)/(num17+num18)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans52", "description": ""}, "ans53": {"definition": "(abs(ans51 - ans52)/ ans52)*100", "templateType": "anything", "group": "Ungrouped variables", "name": "ans53", "description": ""}, "ans51": {"definition": "(siground(num15,1)-siground(num16,1))/(siground(num17,1)+siground(num18,1))", "templateType": "anything", "group": "Ungrouped variables", "name": "ans51", "description": ""}, "num16": {"definition": "random(201..299)", "templateType": "anything", "group": "Ungrouped variables", "name": "num16", "description": ""}, "num17": {"definition": "random(41..59 except 50)", "templateType": "anything", "group": "Ungrouped variables", "name": "num17", "description": ""}, "num14": {"definition": "random(11..25#0.01 except num11)", "templateType": "anything", "group": "Ungrouped variables", "name": "num14", "description": ""}, "num15": {"definition": "hun()", "templateType": "anything", "group": "Ungrouped variables", "name": "num15", "description": ""}, "num12": {"definition": "sin()", "templateType": "anything", "group": "Ungrouped variables", "name": "num12", "description": ""}, "num13": {"definition": "random(3.5..5.5#0.01 except num12)", "templateType": "anything", "group": "Ungrouped variables", "name": "num13", "description": ""}, "num10": {"definition": "random(15..30#0.1 except num8)", "templateType": "anything", "group": "Ungrouped variables", "name": "num10", "description": ""}, "num11": {"definition": "precround(tens(),1)", "templateType": "anything", "group": "Ungrouped variables", "name": "num11", "description": ""}, "num18": {"definition": "random(201..299 except num16)", "templateType": "anything", "group": "Ungrouped variables", "name": "num18", "description": ""}, "num19": {"definition": "sin()", "templateType": "anything", "group": "Ungrouped variables", "name": "num19", "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"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}]}]}], "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}]}