// Numbas version: finer_feedback_settings
{"name": "3. Rounding to \\(n\\) decimal places", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "3. Rounding to \\(n\\) decimal places", "tags": [], "metadata": {"description": "<p>Round a number to $n$ decimal places. Part of HELM Book 1.1</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<h3>3 Rounding to <!--l. 370\n--> \\(n\\) decimal places</h3>\n<!--l. 371\n-->\n<p class=\"noindent\">In general, a calculator or computer is unable to store every decimal place of a real number. Real numbers are <strong> rounded </strong> . To round a number to <!--l. 373\n--> \\(n\\) decimal places we look at the <!--l. 373\n--> \\((n+1)^{\\text{th}}\\) digit in the decimal expansion of the number.</p>\n<ul class=\"itemize1\">\n<li class=\"itemize\">If the <!--l. 376\n--> \\((n+1)^{\\text{th}}\\) digit is \\(0\\), \\(1\\), \\(2\\), \\(3\\) or \\(4\\) then we <strong> round down </strong> : that is, we simply chop to <!--l. 377\n--> \\(n\\) places. (In other words we neglect the <!--l. 378\n--> \\((n+1)^{\\text{th}}\\) digit and any digits to its right.)</li>\n<li class=\"itemize\">If the <!--l. 380\n--> \\((n+1)^{\\text{th}}\\) digit is \\(5\\), \\(6\\), \\(7\\), \\(8\\) or \\(9\\) then we <strong> round up </strong> : we add <!--l. 381\n--> \\(1\\) to the <!--l. 381\n--> \\(n^{\\text{th}}\\) decimal place and then chop to <!--l. 382\n--> \\(n\\) places.</li>\n</ul>\n<!--l. 384\n-->\n<p class=\"noindent\">For example</p>\n<!--l. 385\n-->\n<p class=\"noindent\"><!--l. 385\n--> \\begin{align} \\frac13&amp;=0.3333\\qquad\\text{rounded to }4\\text{ decimal places}\\\\ \\frac83&amp;=2.66667\\qquad\\text{rounded to }5\\text{ decimal places}\\\\\\pi&amp;=3.412\\qquad\\text{rounded to }3\\text{ decimal places}\\\\2.3403&amp;=2.340\\qquad\\text{rounded to }3\\text{ decimal places}\\end{align}</p>\n<!--l. 399\n-->\n<p class=\"noindent\">Sometimes the phrase &lsquo;decimal places&rsquo;&nbsp;is abbreviated to &lsquo;d.p.&rsquo;&nbsp;or &lsquo;dec.pl.&rsquo;.</p>\n<!--l. 402\n-->\n<h5><strong>Example 2</strong></h5>\n<!--l. 403\n-->\n<p class=\"noindent\">Write down each of these numbers rounded to \\(4\\) decimal places: <br class=\"newline\"/><br/><!--l. 404\n--> \\(0.12345,\\;-0.44444,\\; 0.5555555,\\; 0.000127351,\\;0.000005,\\; 123.456789\\)</p>\n<!--l. 406\n-->\n<h5><strong>Solution</strong></h5>\n<!--l. 406\n-->\n<p>\\(0.1235,\\;-0.4444,\\; 0.5556,\\; 0.0001,\\;0.0000,\\; 123.4568\\)</p>\n<p class=\"noindent\"><!--l. 406\n--></p>", "advice": "", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "precround(random(-50..50 #0.00000001),random(4..7))", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a"], "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>Write down \\(\\var{a}\\) to \\(3\\) decimal places.</p>\n<p>Answer: [[0]]</p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "Answer", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "precround(a,3)", "maxValue": "precround(a,3)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "Don Shearman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/680/"}, {"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}], "resources": []}]}], "contributors": [{"name": "Don Shearman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/680/"}, {"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}]}