// Numbas version: exam_results_page_options
{"name": "Rounding to decimals places", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["w2", "w2a", "w22", "f2", "f2a", "f2b", "dp", "dp1"], "name": "Rounding to decimals places", "tags": [], "preamble": {"css": "", "js": ""}, "advice": "<div class=\"example\">\n<p>When rounding a number to a certain number of decimal places&nbsp;it is important to recall:</p>\n<ul class=\"bs-content-rb-simplelist\">\n<li>If the next number is <strong>5 or more</strong>, we <strong>round up</strong>.</li>\n<li>If the next number is <strong>4 or less</strong>, we <strong>do not round up</strong>.</li>\n</ul>\n<p>You round the number that is immediately to the right of the digit you are wanting to cut the decimal number at.</p>\n<p>For example 12.3456 rounds to 12.35 to two decimal places because the third decimal place is 5, therefore the previous digit, 4, is rounded up to a 5.</p>\n<p>For more help, check this video - &nbsp; &nbsp;&nbsp;</p>\n<p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;<iframe width=\"500\" height=\"375\" src=\"//www.youtube.com/embed/bdJAak8YCCg\"></iframe></p>\n<h3></h3>\n</div>", "rulesets": {}, "parts": [{"stepsPenalty": 0, "prompt": "<p>Round the following decimals to&nbsp;the nearest whole number (0 decimal places):</p>\n<p>$\\var{w2}$=[[0]]</p>\n<p>$\\var{w2a}$=[[1]]</p>\n<p>$\\var{w22}$=[[2]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>Look at the digit immediately to the right of the boundary (where you are wanting to cut the number at)&nbsp;</p>\n<p><em>If it is 5 or more, round up, otherwise round down.</em></p>\n<p>To round to a whole number you look at the first decimal place to determine whether you round up or down. If the first decimal place is a 5 or more then you round up (increase the units column by 1) and discard the decimals. If the first decimal 4 or less then you round down (leave the units column as it is) and discard the decimals.</p>\n<p>For example:</p>\n<ul>\n<li>123.49 is&nbsp;123 to the nearest whole number</li>\n<li>123.5 is 124 to the nearest whole number</li>\n</ul>\n<p>Note: we only look at the first decimal place when rounding to whole numbers (the others are irrelevant).&nbsp;For example,&nbsp;123.4998 is&nbsp;still rounded to 123. &nbsp;</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"precisionType": "dp", "integerPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "w2", "strictPrecision": true, "minValue": "w2", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "integerPartialCredit": 0, "precisionMessage": "<p>You have not given your answer to the correct precision.</p>", "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "w2a", "strictPrecision": true, "minValue": "w2a", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": 0, "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": "w22", "strictPrecision": true, "minValue": "w22", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": 0, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"stepsPenalty": 0, "prompt": "<p>Round the following decimals to {dp} decimal place<span data-jme-visible=\"{dp}=2 or {dp}=3 or {dp}=4\">s</span>:</p>\n<p>$\\var{f2}$=[[0]]</p>\n<p>$\\var{f2a}$=[[1]]</p>\n<p>$\\var{f2b}$=[[2]]</p>\n<p></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>Since you are rounding to $\\var{dp}$ decimal places we look at the&nbsp;decimal place to the right of this to determine if we round up or down.&nbsp;If the decimal place to the right is a 5 or more then you round up (increase the decimal place to the left by 1) and discard the digits to the right. If the decimal place to the right is 4 or less then you round down (leave the decimal place to the left as it is) and discard the digits to the right.</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "gaps": [{"precisionType": "dp", "precisionMessage": "<p>You have not given your answer to the correct precision.</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "f2", "strictPrecision": true, "minValue": "f2", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "{dp}", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "<p>You have not given your answer to the correct precision.</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "f2a", "strictPrecision": true, "minValue": "f2a", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "{dp}", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "f2b", "strictPrecision": true, "minValue": "f2b", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "{dp}", "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "extensions": [], "statement": "<p>When rounding a number to a certain number of decimal places&nbsp;it is important to recall:</p>\n<ul class=\"bs-content-rb-simplelist\">\n<li>If the next number is <strong>5 or more</strong>, we <strong>round up</strong>.</li>\n<li>If the next number is <strong>4 or less</strong>, we <strong>do not round up</strong>.</li>\n</ul>\n<p>In the following questions, round the given&nbsp;decimals to&nbsp;the given number of decimal places.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"f2b": {"definition": "w2+w22+0.00498", "templateType": "anything", "group": "Ungrouped variables", "name": "f2b", "description": ""}, "f2a": {"definition": "w2a+0.00324", "templateType": "anything", "group": "Ungrouped variables", "name": "f2a", "description": ""}, "dp1": {"definition": "dp+1", "templateType": "anything", "group": "Ungrouped variables", "name": "dp1", "description": ""}, "w2a": {"definition": "random(12.08..475.08#0.1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "w2a", "description": ""}, "f2": {"definition": "w2+w2a+0.00563", "templateType": "anything", "group": "Ungrouped variables", "name": "f2", "description": ""}, "w22": {"definition": "random(13.01..858.99#0.02)", "templateType": "randrange", "group": "Ungrouped variables", "name": "w22", "description": ""}, "w2": {"definition": "random(12.01..980.99#0.04)", "templateType": "randrange", "group": "Ungrouped variables", "name": "w2", "description": ""}, "dp": {"definition": "random(1..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "dp", "description": ""}}, "metadata": {"description": "<p>This exercise will help you round off decimals to given decimal places.</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": "Sarah Turner", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/881/"}]}]}], "contributors": [{"name": "Sarah Turner", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/881/"}]}