// Numbas version: finer_feedback_settings
{"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": [{"variables": {"m": {"definition": "random(1..n-1)", "description": "", "name": "m", "templateType": "anything", "group": "Ungrouped variables"}, "a": {"definition": "random(0..1#0.1 except[0,1])", "description": "", "name": "a", "templateType": "anything", "group": "Ungrouped variables"}, "h": {"definition": "random(1..j-1)", "description": "", "name": "h", "templateType": "anything", "group": "Ungrouped variables"}, "j": {"definition": "random([2,4,5,8,10,20,25,40,50,100,200,400,1000] except g)", "description": "", "name": "j", "templateType": "anything", "group": "Ungrouped variables"}, "l": {"definition": "random([2,4,5,8,10,20,25,40,50,100,200,400,1000] except j)", "description": "", "name": "l", "templateType": "anything", "group": "Ungrouped variables"}, "n": {"definition": "random([3,6,9])", "description": "", "name": "n", "templateType": "anything", "group": "Ungrouped variables"}, "k": {"definition": "random(1..l-1)", "description": "", "name": "k", "templateType": "anything", "group": "Ungrouped variables"}, "g": {"definition": "random([2,4,5,10,20,25,50,100,200,1000])", "description": "", "name": "g", "templateType": "anything", "group": "Ungrouped variables"}, "b": {"definition": "random(0.21..0.99#0.02)", "description": "", "name": "b", "templateType": "randrange", "group": "Ungrouped variables"}, "c": {"definition": "random(0.119..0.999#0.002)", "description": "", "name": "c", "templateType": "randrange", "group": "Ungrouped variables"}, "d": {"definition": "random(0.11..0.2#0.02)", "description": "", "name": "d", "templateType": "randrange", "group": "Ungrouped variables"}, "f": {"definition": "random(1..g-1)", "description": "", "name": "f", "templateType": "anything", "group": "Ungrouped variables"}}, "ungrouped_variables": ["a", "b", "c", "d", "f", "g", "h", "j", "k", "l", "m", "n"], "parts": [{"gaps": [{"mustBeReduced": false, "marks": 1, "showCorrectAnswer": true, "scripts": {}, "showFeedbackIcon": true, "type": "numberentry", "mustBeReducedPC": 0, "minValue": "(a*10)/10", "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "variableReplacements": [], "maxValue": "(a*10)/10", "allowFractions": true, "notationStyles": ["plain", "en", "si-en"]}, {"mustBeReduced": false, "marks": 1, "showCorrectAnswer": true, "scripts": {}, "showFeedbackIcon": true, "type": "numberentry", "mustBeReducedPC": 0, "minValue": "(b*100)/100", "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "variableReplacements": [], "maxValue": "(b*100)/100", "allowFractions": true, "notationStyles": ["plain", "en", "si-en"]}, {"mustBeReduced": false, "marks": 1, "showCorrectAnswer": true, "scripts": {}, "showFeedbackIcon": true, "type": "numberentry", "mustBeReducedPC": 0, "minValue": "(c*1000)/1000", "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "variableReplacements": [], "maxValue": "(c*1000)/1000", "allowFractions": true, "notationStyles": ["plain", "en", "si-en"]}, {"mustBeReduced": false, "marks": 1, "showCorrectAnswer": true, "scripts": {}, "showFeedbackIcon": true, "type": "numberentry", "mustBeReducedPC": 0, "minValue": "(d*100)/100", "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "variableReplacements": [], "maxValue": "(d*100)/100", "allowFractions": true, "notationStyles": ["plain", "en", "si-en"]}], "steps": [{"marks": 0, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "scripts": {}, "type": "information", "variableReplacements": [], "showCorrectAnswer": true, "prompt": "<ul>\n<li><b>Step 1:</b>&nbsp;Write the decimal value as the numerator of a fraction with 1 as the denominator:&nbsp;e.g. $\\frac{0.52}{1}$</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. If there are two&nbsp;digits after the decimal point, then use 100, if there are three then use 1000, and so on. The aim here is to ensure the numerator becomes a natural number without decimal digits:&nbsp;e.g. $\\frac{0.52}{1}\\times\\frac{100}{100}=\\frac{52}{100}$</li>\n<li><b>Step 3:</b>&nbsp;Simplify&nbsp;(or reduce) the fraction: e.g. $\\frac{52}{100}=\\frac{26}{50}=\\frac{13}{25}$</li>\n</ul>"}], "marks": 0, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "scripts": {}, "type": "gapfill", "variableReplacements": [], "showCorrectAnswer": true, "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>"}, {"gaps": [{"mustBeReduced": false, "marks": 1, "showCorrectAnswer": true, "precisionMessage": "You have not given your answer to the correct precision.", "scripts": {}, "showFeedbackIcon": true, "type": "numberentry", "precision": "2", "strictPrecision": false, "mustBeReducedPC": 0, "minValue": "f/g", "precisionPartialCredit": 0, "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "variableReplacements": [], "showPrecisionHint": false, "maxValue": "f/g", "allowFractions": false, "precisionType": "dp"}, {"mustBeReduced": false, "marks": 1, "showCorrectAnswer": true, "precisionMessage": "You have not given your answer to the correct precision.", "scripts": {}, "showFeedbackIcon": true, "type": "numberentry", "precision": "2", "strictPrecision": false, "mustBeReducedPC": 0, "minValue": "h/j", "precisionPartialCredit": 0, "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "variableReplacements": [], "showPrecisionHint": false, "maxValue": "h/j", "allowFractions": false, "precisionType": "dp"}, {"mustBeReduced": false, "marks": 1, "showCorrectAnswer": true, "precisionMessage": "You have not given your answer to the correct precision.", "scripts": {}, "showFeedbackIcon": true, "type": "numberentry", "precision": "2", "strictPrecision": false, "mustBeReducedPC": 0, "minValue": "k/l", "precisionPartialCredit": 0, "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "variableReplacements": [], "showPrecisionHint": false, "maxValue": "k/l", "allowFractions": false, "precisionType": "dp"}, {"mustBeReduced": false, "marks": 1, "showCorrectAnswer": true, "precisionMessage": "You have not given your answer to the correct precision.", "scripts": {}, "showFeedbackIcon": true, "type": "numberentry", "precision": "2", "strictPrecision": false, "mustBeReducedPC": 0, "minValue": "m/n", "precisionPartialCredit": 0, "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "variableReplacements": [], "showPrecisionHint": false, "maxValue": "m/n", "allowFractions": false, "precisionType": "dp"}], "steps": [{"marks": 0, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "scripts": {}, "type": "information", "variableReplacements": [], "showCorrectAnswer": true, "prompt": "<ul>\n<li><b>Step 1</b>: Find a number you can multiply the denominator&nbsp;by to make it either 10 if there is one digit in the numerator, 100 if there are two, 1000 if there are three, and so on: e.g. for $\\frac{3}{5}$, there is one digit in the numerator so we need to find a value which multiplies the denominator to make 10. In this case, we need the number 2.</li>\n<li><b>Step 2</b>: Multiply both the numerator and denominator by that number: $\\frac{3}{5}\\times\\frac{6}{10}$</li>\n<li><b>Step 3</b>. Write the numerator with the decimal point in front of the first digit to give the equivalent decimal form: e.g. $\\frac{6}{10}=0.6$</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>"}], "marks": 0, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "scripts": {}, "type": "gapfill", "variableReplacements": [], "showCorrectAnswer": true, "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>"}], "variablesTest": {"condition": "", "maxRuns": 100}, "tags": [], "functions": {}, "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><strong>Step 1:</strong>&nbsp;Write the decimal value as the numerator of a fraction with 1 as the denominator:&nbsp;e.g. $\\frac{0.52}{1}$</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. If there are two&nbsp;digits after the decimal point, then use 100, if there are three then use 1000, and so on. The aim here is to ensure the numerator becomes a natural number without decimal digits:&nbsp;e.g. $\\frac{0.52}{1}\\times\\frac{100}{100}=\\frac{52}{100}$</li>\n<li><b>Step 3:</b>&nbsp;Simplify&nbsp;(or reduce) the fraction: e.g. $\\frac{52}{100}=\\frac{26}{50}=\\frac{13}{25}$</li>\n</ul>\n<p>To convert fractions to decimals, follow these steps:</p>\n<ul>\n<li><strong>Step 1</strong>: Find a number you can multiply the denominator&nbsp;by to make it either 10 if there is one digit in the numerator, 100 if there are two, 1000 if there are three, and so on: e.g. for $\\frac{3}{5}$, there is one digit in the numerator so we need to find a value which multiplies the denominator to make 10. In this case, we need the number 2.</li>\n<li><b>Step 2</b>: Multiply both the numerator and denominator by that number: $\\frac{3}{5}\\times\\frac{6}{10}$</li>\n<li><b>Step 3</b>. Write the numerator with the decimal point in front of the first digit to give the equivalent decimal form: e.g. $\\frac{6}{10}=0.6$</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>", "preamble": {"css": "", "js": ""}, "name": "Numbers IV: conversions (decimals and fractions)", "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>", "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"}, "rulesets": {}, "variable_groups": [], "type": "question", "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/"}]}