// Numbas version: finer_feedback_settings
{"name": " Conversions - Decimals and Fractions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["a", "b", "c", "d", "f", "g", "h", "j", "k", "l", "m", "n"], "name": " Conversions - Decimals and Fractions", "tags": [], "preamble": {"css": "", "js": ""}, "advice": "<p>Fractions and decimals represent the same things: numbers that are not whole numbers.</p>\n<p>To convert decimals to fractions, simply follow these steps:</p>\n<ul>\n<li>Step 1: Write down the decimal divided by 1, like this: &nbsp; Decimal<em> /&nbsp;</em><span class=\"large\"><span class=\"intbl\">1</span></span></li>\n<li>Step 2: Multiply both top and bottom by 10 for every number after the decimal point. (For example, if there are two numbers after the decimal point, then use 100, if there are three then use 1000, etc.)</li>\n<li>Step 3: <a href=\"https://www.mathsisfun.com/simplifying-fractions.html\">Simplify</a> (or reduce) the fraction</li>\n</ul>\n<p>To convert fractions to decimals, simply follow these steps:</p>\n<ul>\n<li>Step 1: Find a number you can multiply by the bottom of the fraction to make it 10, or 100, or 1000, or any <span color=\"#0000ff\" style=\"color: #0000ff;\">1 followed by 0s</span>.</li>\n<li>Step 2: Multiply both top and bottom by that number.</li>\n<li>Step 3. Then write down just the top number, putting the decimal point in the correct spot (one space from the right hand side for every zero in the bottom number)</li>\n</ul>\n<div class=\"example\"></div>", "rulesets": {}, "parts": [{"stepsPenalty": 0, "prompt": "<p>Give a fraction which is equivalent to these decimals:</p>\n<p>$\\var{a}$ = [[0]]</p>\n<p>$\\var{b}$ = [[1]]</p>\n<p>$\\var{c}$ = [[2]]</p>\n<p>$\\var{d}$ = [[3]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<ul>\n<li><b>Step 1:</b> Write down the decimal divided by 1, like this: Decimal /&nbsp;<span class=\"large\"><span class=\"intbl\"><strong>1</strong></span></span></li>\n<li><b>Step 2:</b> Multiply both top and bottom by 10 for every number after the decimal point. (For example, if there are two numbers after the decimal point, then use 100, if there are three then use 1000, etc.)</li>\n<li><b>Step 3:</b>&nbsp;Simplify&nbsp;(or reduce) the fraction</li>\n</ul>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"allowFractions": true, "variableReplacements": [], "maxValue": "(a*10)/10", "minValue": "(a*10)/10", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": true, "variableReplacements": [], "maxValue": "(b*100)/100", "minValue": "(b*100)/100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": true, "variableReplacements": [], "maxValue": "(c*1000)/1000", "minValue": "(c*1000)/1000", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": true, "variableReplacements": [], "maxValue": "(d*100)/100", "minValue": "(d*100)/100", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": 0, "prompt": "<p>Give the decimal that is equivalent to these fractions:</p>\n<p>$\\frac{\\var{f}}{\\var{g}}$ = [[0]]</p>\n<p>$\\frac{\\var{h}}{\\var{j}}$ = [[1]]</p>\n<p>$\\frac{\\var{k}}{\\var{l}}$ = [[2]]</p>\n<p>$\\frac{\\var{m}}{\\var{n}}$ = [[3]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<ul>\n<li><b>Step 1</b>: Find a number you can multiply by the bottom of the fraction to make it 10, or 100, or 1000, or any 1 followed by 0s.</li>\n<li><b>Step 2</b>: Multiply both top and bottom by that number.</li>\n<li><b>Step 3</b>. Then write down just the top number, putting the decimal point in the correct spot (one space from the right hand side for every zero in the bottom number)</li>\n</ul>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "f/g", "minValue": "f/g", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "h/j", "minValue": "h/j", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "k/l", "minValue": "k/l", "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": "m/n", "strictPrecision": false, "minValue": "m/n", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "3", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": 0, "maxAnswers": 0, "prompt": "<p>Match any pairs of fractions and decimals (you might not use all of the&nbsp;options).</p>", "matrix": [["1", 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, "1", 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, "1", 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, "1", 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, "1", 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, "1", 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, "1", 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, "1", 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, "1", 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, "1", 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], "shuffleAnswers": true, "minAnswers": "0", "maxMarks": "10", "variableReplacements": [], "displayType": "radiogroup", "answers": ["<p>$\\frac{1}{2}$</p>", "<p>$\\frac{1}{4}$</p>", "<p>$\\frac{1}{5}$</p>", "<p>$\\frac{1}{10}$</p>", "<p>$\\frac{1}{8}$</p>", "<p>$\\frac{1}{20}$</p>", "<p>$\\frac{1}{25}$</p>", "<p>$\\frac{1}{100}$</p>", "<p>$\\frac{1}{3}$</p>", "<p>$\\frac{1}{9}$</p>", "<p>$\\frac{3}{4}$</p>", "<p>$\\frac{2}{5}$</p>", "<p>$\\frac{1}{11}$</p>", "<p>$\\frac{1}{33}$</p>", "<p>$\\frac{1}{01}$</p>"], "warningType": "none", "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<ul>\n<li><b>Step 1:</b> Write down the decimal divided by 1, like this: Decimal /&nbsp;<span class=\"large\"><span class=\"intbl\"><strong>1</strong></span></span></li>\n<li><b>Step 2:</b> Multiply both top and bottom by 10 for every number after the decimal point. (For example, if there are two numbers after the decimal point, then use 100, if there are three then use 1000, etc.)</li>\n<li><b>Step 3:</b>&nbsp;Simplify&nbsp;(or reduce) the fraction.</li>\n</ul>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "choices": ["<p>$0.5$</p>", "<p>$0.25$</p>", "<p>$0.2$</p>", "<p>$0.1$</p>", "<p>$0.125$</p>", "<p>$0.05$</p>", "<p>$0.04$</p>", "<p>$0.01$</p>", "<p>$0.3\\dot{3}$</p>", "<p>$0.1\\dot{1}$</p>", "<p>$0.6$</p>", "<p>$0.3$</p>", "<p>$0.85$</p>", "<p>$0.6\\dot{6}$</p>", "<p>$0.45$</p>"], "type": "m_n_x", "shuffleChoices": true, "minMarks": "10", "layout": {"expression": "", "type": "all"}}], "extensions": [], "statement": "<p>This test has three parts which deal with the conversion of decimals to fractions and vice-versa.</p>\n<p>Please attempt all the questions and for further guidance, please check this video-&nbsp;<a href=\"https://www.youtube.com/watch?v=Yca7BpcMRpI\">https://www.youtube.com/watch?v=Yca7BpcMRpI</a></p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(0..1#0.1 except[0,1])", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "random(0..1#0.001 except [0,1])", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(0..1#0.01 except[0,1])", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "random(1..2#0.01 except [1,2])", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "g": {"definition": "random([2,4,5,10,20,25,50,100,200,1000])", "templateType": "anything", "group": "Ungrouped variables", "name": "g", "description": ""}, "f": {"definition": "random(1..g-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "f", "description": ""}, "h": {"definition": "random(1..j-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "h", "description": ""}, "k": {"definition": "random(1..l-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "k", "description": ""}, "j": {"definition": "random([2,4,5,8,10,20,25,40,50,100,200,400,1000] except g)", "templateType": "anything", "group": "Ungrouped variables", "name": "j", "description": ""}, "m": {"definition": "random(1..n-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "m", "description": ""}, "l": {"definition": "random([2,4,5,8,10,20,25,40,50,100,200,400,1000] except j)", "templateType": "anything", "group": "Ungrouped variables", "name": "l", "description": ""}, "n": {"definition": "random([3,6,9])", "templateType": "anything", "group": "Ungrouped variables", "name": "n", "description": ""}}, "metadata": {"description": "<p>These short questions allow you to practice converting between decimals and fractions</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Nasir Firoz Khan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/909/"}]}]}], "contributors": [{"name": "Nasir Firoz Khan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/909/"}]}