// Numbas version: exam_results_page_options
{"name": "Decimals: how to read", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Decimals: how to read", "tags": [], "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>If you are unsure of how to do&nbsp;a question, click on&nbsp;<em>Show steps</em>&nbsp;to see the full working. Then, once you understand how to do the question, click on&nbsp;<em>Try another question like this one</em>&nbsp;to start again.</p>", "advice": "", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"place": {"name": "place", "group": "Ungrouped variables", "definition": "random([placedig*0.001, \"tenths\", \"hundredths\", \"thousandths\" ]\n,[placedig*0.01, \"tenths\", \"thousandths\", \"hundredths\"],\n  [placedig*0.1,  \"thousandths\", \"hundredths\", \"tenths\"])", "description": "", "templateType": "anything", "can_override": false}, "pron": {"name": "pron", "group": "Ungrouped variables", "definition": "shuffle([random(\n[dpformat(0.10, 2), \"one zero\", \"ten\"],  \n[dpformat(0.11, 2), \"one one\", \"eleven\"],  \n[dpformat(0.12, 2), \"one two\", \"twelve\"],\n[dpformat(0.13, 2), \"one three\", \"thirteen\"],\n[dpformat(0.14, 2), \"one four\", \"fourteen\"],\n[dpformat(0.15, 2), \"one five\", \"fifteen\"],\n[dpformat(0.16, 2), \"one six\", \"sixteen\"],\n[dpformat(0.17, 2), \"one seven\", \"seventeen\"],\n[dpformat(0.18, 2), \"one eight\", \"eighteen\"],\n[dpformat(0.19, 2), \"one nine\", \"ninteen\"], \n\n[dpformat(0.20, 2), \"two zero\", \"twenty\"],  \n[dpformat(0.21, 2), \"two one\", \"twenty one\"],  \n[dpformat(0.22, 2), \"two two\", \"twenty two\"],\n[dpformat(0.23, 2), \"two three\", \"twenty three\"],\n[dpformat(0.24, 2), \"two four\", \"twenty four\"], \n[dpformat(0.25, 2), \"two five\", \"twenty five\"],\n[dpformat(0.26, 2), \"two six\", \"twenty six\"],\n[dpformat(0.27, 2), \"two seven\", \"twenty seven\"],\n[dpformat(0.28, 2), \"two eight\", \"twenty eight\"],\n[dpformat(0.29, 2), \"two nine\", \"twenty nine\"],   \n  \n[dpformat(0.30, 2), \"three zero\", \"thirty\"],  \n[dpformat(0.31, 2), \"three one\", \"thirty one\"],  \n[dpformat(0.32, 2), \"three two\", \"thirty two\"],\n[dpformat(0.33, 2), \"three three\", \"thirty three\"],\n[dpformat(0.34, 2), \"three four\", \"thirty four\"], \n[dpformat(0.35, 2), \"three five\", \"thirty five\"],\n[dpformat(0.36, 2), \"three six\", \"thirty six\"],\n[dpformat(0.37, 2), \"three seven\", \"thirty seven\"],\n[dpformat(0.38, 2), \"three eight\", \"thirty eight\"],\n[dpformat(0.39, 2), \"three nine\", \"thirty nine\"],  \n  \n[dpformat(0.40, 2), \"four zero\", \"forty\"],  \n[dpformat(0.41, 2), \"four one\", \"forty one\"],  \n[dpformat(0.42, 2), \"four two\", \"forty two\"],\n[dpformat(0.43, 2), \"four three\", \"forty three\"],\n[dpformat(0.44, 2), \"four four\", \"forty four\"], \n[dpformat(0.45, 2), \"four five\", \"forty five\"],\n[dpformat(0.46, 2), \"four six\", \"forty six\"],\n[dpformat(0.47, 2), \"four seven\", \"forty seven\"],\n[dpformat(0.48, 2), \"four eight\", \"forty eight\"],\n[dpformat(0.49, 2), \"four nine\", \"forty nine\"], \n  \n[dpformat(0.50, 2), \"five zero\", \"fifty\"],  \n[dpformat(0.51, 2), \"five one\", \"fifty one\"],  \n[dpformat(0.52, 2), \"five two\", \"fifty two\"],\n[dpformat(0.53, 2), \"five three\", \"fifty three\"],\n[dpformat(0.54, 2), \"five four\", \"fifty four\"], \n[dpformat(0.55, 2), \"five five\", \"fifty five\"],\n[dpformat(0.56, 2), \"five six\", \"fifty six\"],\n[dpformat(0.57, 2), \"five seven\", \"fifty seven\"],\n[dpformat(0.58, 2), \"five eight\", \"fifty eight\"],\n[dpformat(0.59, 2), \"five nine\", \"fifty nine\"], \n  \n[dpformat(0.60, 2), \"six zero\", \"sixty\"],  \n[dpformat(0.70, 2), \"seven zero\", \"seventy\"],  \n[dpformat(0.80, 2), \"eight zero\", \"eighty\"],  \n[dpformat(0.90, 2), \"nine zero\", \"ninety\"],  \n)]+[random(\n[dpformat(0.100, 3), \"one zero zero\", \"one hundred\"],  \n[dpformat(0.200, 3), \"two zero zero\", \"two hundred\"],  \n[dpformat(0.300, 3), \"three zero zero\", \"three hundred\"],\n[dpformat(0.400, 3), \"four zero zero\", \"four hundred\"],\n[dpformat(0.500, 3), \"five zero zero\", \"five hundred\"], \n[dpformat(0.600, 3), \"six zero zero\", \"six hundred\"],\n[dpformat(0.700, 3), \"seven zero zero\", \"seven hundred\"],\n[dpformat(0.800, 3), \"eight zero zero\", \"eight hundred\"],\n[dpformat(0.900, 3), \"nine zero zero\", \"nine hundred\"],\n[dpformat(0.120, 3), \"one two zero\", \"one hundred and twenty\"],  \n[dpformat(0.230, 3), \"two three zero\", \"two hundred and thirty\"],  \n[dpformat(0.340, 3), \"three four zero\", \"three hundred and forty\"],\n[dpformat(0.450, 3), \"four five zero\", \"four hundred and fifty\"],\n[dpformat(0.501, 3), \"five zero one\", \"five hundred and one\"], \n[dpformat(0.602, 3), \"six zero two\", \"six hundred and two\"],\n[dpformat(0.703, 3), \"seven zero three\", \"seven hundred and three\"],\n[dpformat(0.804, 3), \"eight zero four\", \"eight hundred and four\"],\n[dpformat(0.905, 3), \"nine zero five\", \"nine hundred and five\"]\n  )])\n ", "description": "", "templateType": "anything", "can_override": false}, "placedig": {"name": "placedig", "group": "Ungrouped variables", "definition": "random(1..9)", "description": "", "templateType": "anything", "can_override": false}, "hundredths": {"name": "hundredths", "group": "Ungrouped variables", "definition": "if(len(pron[0][0])=4,dec(pron[0][0])*100,dec(pron[1][0])*100)", "description": "", "templateType": "anything", "can_override": false}, "pron2": {"name": "pron2", "group": "Ungrouped variables", "definition": "random(\n[dpformat(0.100, 3), \"zero point one zero zero\", \"zero point one hundred\"],  \n[dpformat(0.200, 3), \"zero point two zero zero\", \"zero point two hundred\"],  \n[dpformat(0.300, 3), \"zero point three zero zero\", \"zero point three hundred\"],\n[dpformat(0.400, 3), \"zero point four zero zero\", \"zero point four hundred\"],\n[dpformat(0.500, 3), \"zero point five zero zero\", \"zero point five hundred\"], \n[dpformat(0.600, 3), \"zero point six zero zero\", \"zero point six hundred\"],\n[dpformat(0.700, 3), \"zero point seven zero zero\", \"zero point seven hundred\"],\n[dpformat(0.800, 3), \"zero point eight zero zero\", \"zero point eight hundred\"],\n[dpformat(0.900, 3), \"zero point nine zero zero\", \"zero point nine hundred\"],\n[dpformat(0.120, 3), \"zero point one two zero\", \"zero point one hundred and twenty\"],  \n[dpformat(0.230, 3), \"zero point two three zero\", \"zero point two hundred and thirty\"],  \n[dpformat(0.340, 3), \"zero point three four zero\", \"zero point three hundred and forty\"],\n[dpformat(0.450, 3), \"zero point four five zero\", \"zero point four hundred and fifty\"],\n[dpformat(0.501, 3), \"zero point five zero one\", \"zero point five hundred and one\"], \n[dpformat(0.602, 3), \"zero point six zero two\", \"zero point six hundred and two\"],\n[dpformat(0.703, 3), \"zero point seven zero three\", \"zero point seven hundred and three\"],\n[dpformat(0.804, 3), \"zero point eight zero four\", \"zero point eight hundred and four\"],\n[dpformat(0.905, 3), \"zero point nine zero five\", \"zero point nine hundred and five\"]\n  )", "description": "", "templateType": "anything", "can_override": false}, "thousandths": {"name": "thousandths", "group": "Ungrouped variables", "definition": "if(len(pron[0][0])=5,dec(pron[0][0])*1000,dec(pron[1][0])*1000)", "description": "", "templateType": "anything", "can_override": false}, "identify": {"name": "identify", "group": "Ungrouped variables", "definition": "if(len(pron[0][0])=5,[[1000,dec(pron[0][0])*1000],[100, dec(pron[1][0])*100]],[[100, dec(pron[0][0])*100],[1000,dec(pron[1][0])*1000]])", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["placedig", "place", "pron", "identify", "thousandths", "hundredths", "pron2"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>The digit $\\var{placedig}$ in the decimal $\\var{place[0]}$ represents&nbsp;&nbsp;[[0]]</p>", "stepsPenalty": "1", "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p style=\"text-align: left;\">The decimal 0.1 is also known as \"one tenth\" (notice you need ten of them to make a whole).</p>\n<p>The decimal 0.01 is also known as \"one hundredth\" (notice you need a hundred&nbsp;of them to make a whole).</p>\n<p>The decimal 0.001 is also known as \"one thousandth\" (notice you need a thousand&nbsp;of them to make a whole).</p>\n<p></p>\n<hr/>\n<p></p>\n<p>That is,&nbsp;the digit $\\var{placedig}$ in the decimal $\\var{place[0]}$ is in the {place[3]} column and so represents $\\var{placedig}$ {place[3]}.</p>"}], "gaps": [{"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": "1", "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["<p>$\\var{placedig}$ {place[1]}</p>", "<p>$\\var{placedig}$ {place[2]}</p>", "<p>$\\var{placedig}$ {place[3]}</p>"], "matrix": [0, 0, "1"], "distractors": ["", "", ""]}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>The decimal $\\var{pron[0][0]}$ should be read as [[0]]</p>\n<p>or, as $\\var{identify[0][1]}$ [[1]].</p>\n<p></p>", "stepsPenalty": "2", "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p><em>Say each&nbsp;digit individually&nbsp;after the decimal point.</em></p>\n<p></p>\n<hr/>\n<p></p>\n<p>It makes no sense to call 0.500, \"zero point five hundred\"&nbsp;since that sounds a lot bigger than \"zero <g class=\"gr_ gr_9 gr-alert gr_gramm Grammar multiReplace\" id=\"9\" data-gr-id=\"9\">point</g> five\", or \"zero <g class=\"gr_ gr_10 gr-alert gr_gramm Grammar multiReplace\" id=\"10\" data-gr-id=\"10\">point</g> fifty\", but these are all equal to the same number! Pronouncing decimals like this is misleading and doesn't help with your intuition. However, this decimal is 500 of something, it is 500 <em>thousandths!</em> But be careful, even reading it that way can be ambiguous when it's read aloud.&nbsp;</p>\n<p></p>\n<hr/>\n<p></p>\n<p>That is, $\\var{pron[0][0]}$ is read as <em>{pron[0][1]}</em>.</p>\n<p>Alternatively, since the last digit written is in the <span data-jme-visible=\"identify[0][0]=100\"><em>hundredths</em></span><span data-jme-visible=\"identify[0][0]=1000\"><em>thousandths</em></span> column, we can think of this (and read it out) as&nbsp;$\\var{identify[0][1]}$ <span data-jme-visible=\"identify[0][0]=100\">hundredths.</span><span data-jme-visible=\"identify[0][0]=1000\">thousandths.</span>&nbsp;</p>"}], "gaps": [{"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": "1", "shuffleChoices": true, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["<p>zero point {pron[0][1]}</p>", "<p>zero point {pron[0][2]}</p>"], "matrix": ["1", 0], "distractors": ["", "Please see the steps"]}, {"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["tenths", "hundredths", "thousandths"], "matrix": [0, "if(identify[0][0]=100,1,0)", "if(identify[0][0]=1000,1,0)"], "distractors": ["", "", ""]}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>The decimal $\\var{pron[1][0]}$ should be read as [[0]]</p>\n<p>or, as $\\var{identify[1][1]}$ [[1]].</p>\n<p></p>", "stepsPenalty": "2", "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p><em>Say each&nbsp;digit individually&nbsp;after the decimal point.</em></p>\n<p></p>\n<hr/>\n<p></p>\n<p>It makes no sense to call 0.500, \"zero point five hundred\"&nbsp;since that sounds a lot bigger than \"zero <g class=\"gr_ gr_9 gr-alert gr_gramm Grammar multiReplace\" id=\"9\" data-gr-id=\"9\">point</g> five\", or \"zero <g class=\"gr_ gr_10 gr-alert gr_gramm Grammar multiReplace\" id=\"10\" data-gr-id=\"10\">point</g> fifty\", but these are all equal to the same number! Pronouncing decimals like this is misleading and doesn't help with your intuition. However, this decimal is 500 of something, it is 500 <em>thousandths!</em> But be careful, even reading it that way can be ambiguous when it's read aloud.&nbsp;</p>\n<p></p>\n<hr/>\n<p></p>\n<p>That is, $\\var{pron[1][0]}$ is read as <em>{pron[1][1]}</em>.</p>\n<p>Alternatively, since the last digit written is in the <span data-jme-visible=\"identify[1][0]=100\"><em>hundredths</em></span><span data-jme-visible=\"identify[1][0]=1000\"><em>thousandths</em></span> column, we can think of this as $\\var{identify[1][1]}$ <span data-jme-visible=\"identify[1][0]=100\">hundredths.</span><span data-jme-visible=\"identify[1][0]=1000\">thousandths.</span>&nbsp;</p>"}], "gaps": [{"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": "1", "shuffleChoices": true, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["<p>zero point {pron[1][1]}</p>", "<p>zero point {pron[1][2]}</p>"], "matrix": ["1", 0], "distractors": ["", "Please see the steps"]}, {"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["tenths", "hundredths", "thousandths"], "matrix": [0, "if(identify[1][0]=100,1,0)", "if(identify[1][0]=1000,1,0)"], "distractors": ["", "", ""]}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}