// Numbas version: exam_results_page_options
{"name": "Numbers IV: 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": "Numbers IV: 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, follow these simple steps:</p>\n<ul>\n<li>Step 1: Write down the decimal divided by 1 - ($\\frac{decimal}{1}$)</li>\n<li>Step 2: Multiply both&nbsp;the numerator and denominator&nbsp;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, follow these steps:</p>\n<ul>\n<li>Step 1: Find a number you can multiply the denominator by to make&nbsp;it 10, 100, or 1000 etc.</li>\n<li>Step 2: Multiply both the numerator and denominator&nbsp;by that number</li>\n<li>Step 3: With your new numerator, convert to a decimal by inserting&nbsp;the decimal point to the correct place as this will you give you the decimal equivalent of the original fraction.</li>\n<li>\n<p>If this is not possible, you could&nbsp;to try long division instead (after simplifying the fraction as much as possible to make the division easier).</p>\n</li>\n</ul>\n<p><iframe width=\"500\" height=\"375\" src=\"//www.youtube.com/embed/Gn2pdkvdbGQ\"></iframe>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;<iframe width=\"500\" height=\"375\" src=\"//www.youtube.com/embed/DR2DYe7PI74\"></iframe></p>\n<div class=\"example\"></div>", "rulesets": {}, "parts": [{"stepsPenalty": 0, "prompt": "<p>Give a<strong> fraction</strong>&nbsp;that&nbsp;is equivalent to the&nbsp;following&nbsp;decimals:</p>\n<p>$\\var{a}$ = &nbsp;[[0]]</p>\n<p>$\\var{b}$ = [[1]]</p>\n<p>$\\var{c}$ = [[2]]</p>\n<p>$\\var{d}$ = [[3]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "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}], "steps": [{"prompt": "<ul>\n<li><b>Step 1:</b> Divide the decimal number by 1 ($\\frac{decimal}{1}$)</li>\n<li><b>Step 2:</b> Multiply both the numerator&nbsp;and the denominator&nbsp;by 10 for every number of places 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"}], "scripts": {}, "marks": 0, "showCorrectAnswer": true, "type": "gapfill"}, {"stepsPenalty": 0, "prompt": "<p>Give the<strong> decimal</strong> that is equivalent to the following fractions: (Give your answer to <strong>2 decimal places</strong>)</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", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "2", "maxValue": "f/g", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "minValue": "f/g", "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "2", "maxValue": "h/j", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "minValue": "h/j", "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "2", "maxValue": "k/l", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "minValue": "k/l", "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "2", "maxValue": "m/n", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": 1, "minValue": "m/n", "type": "numberentry", "showPrecisionHint": false}], "steps": [{"prompt": "<ul>\n<li><b>Step 1</b>: Find a number you can multiply the denominator&nbsp;by to make it either 10, 100,1000 etc.</li>\n<li><b>Step 2</b>: Multiply both the numerator and denominator by that number.</li>\n<li><b>Step 3</b>. With your new numerator, convert to a decimal by inserting&nbsp;the decimal point to the correct place as this will you give you the decimal equivalent of the original fraction.</li>\n</ul>\n<p>If this is not possible, you could&nbsp;to try long division instead (after simplifying the fraction as much as possible to make the division easier).</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": 0, "showCorrectAnswer": true, "type": "gapfill"}], "extensions": [], "statement": "<p>This test has two 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(0.119..0.999#0.002)", "templateType": "randrange", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(0.21..0.99#0.02)", "templateType": "randrange", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "random(0.11..0.2#0.02)", "templateType": "randrange", "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": "Rachel Staddon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/901/"}]}]}], "contributors": [{"name": "Rachel Staddon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/901/"}]}