// Numbas version: finer_feedback_settings
{"name": "4. Rounding to \\(n\\) significant figures", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "4. Rounding to \\(n\\) significant figures", "tags": [], "metadata": {"description": "<p>Round a number to $n$ significant figures. Part of HELM Book 1.1</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<h3>4 Rounding to \\(n\\) significant figures</h3>\n<!--l. 422\n-->\n<p class=\"noindent\">This process is similar to rounding to decimal places but there are some subtle differences.</p>\n<!--l. 424\n-->\n<p class=\"noindent\">To round a number to <!--l. 424\n--> \\(n\\) significant figures we look at the <!--l. 424\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. 427\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. 428\n--> \\(n\\) places, inserting zeros if necessary before the decimal point. (In other words we neglect the <!--l. 429\n--> \\((n+1)^{\\text{th}}\\) digit and any digits to its right.)</li>\n<li class=\"itemize\">If the <!--l. 431\n--> \\((n+1)^{\\text{th}}\\) digit is \\(5\\), \\(6\\), \\(7\\), \\(8\\) or \\(9\\) then we <strong> round up </strong> : we add <!--l. 432\n--> \\(1\\) to the <!--l. 432\n--> \\(n^{\\text{th}}\\) decimal place and then chop to <!--l. 433\n--> \\(n\\) places, inserting zeros if necessary before the decimal point.</li>\n</ul>\n<!--l. 435\n-->\n<p class=\"noindent\">For example:</p>\n<!--l. 436\n-->\n<p class=\"noindent\"><!--l. 436\n--> \\begin{align} \\frac13&amp;=0.3333\\qquad\\text{rounded to }4\\text{ significant figures}\\\\ \\frac83&amp;=2.66667\\qquad\\text{rounded to }6\\text{ significant figures}\\\\\\pi&amp;=3.412\\qquad\\text{rounded to }4\\text{ significant figures}\\\\2136&amp;=2000\\qquad\\text{rounded to }1\\text{ significant figure}\\\\36.78&amp;=37\\qquad\\text{rounded to }2\\text{ significant figures}\\\\6.2399&amp;=6.240\\qquad\\text{rounded to }4\\text{ significant figures}\\end{align}</p>\n<!--l. 457\n-->\n<p class=\"noindent\">Sometimes the phrase &ldquo;significant figures\" is abbreviated as &ldquo;s.f.\" or &ldquo;sig.fig.\"</p>\n<!--l. 461\n-->\n<h5><strong>Example 3</strong></h5>\n<!--l. 462\n-->\n<p class=\"noindent\">Write down each of these numbers, rounding them to 4 significant figures: <br class=\"newline\"/><br/><!--l. 463\n--> \\(0.12345,\\;-0.44444,\\; 0.5555555,\\; 0.000127351,\\;25679,\\; 123.456789,\\; 3456543\\)</p>\n<!--l. 465\n-->\n<h5><strong>Solution</strong></h5>\n<!--l. 465\n-->\n<p class=\"noindent\"><!--l. 465\n--> \\(0.1235,\\;-0.4444,\\; 0.5556,\\; 0.0001274,\\;25680,\\; 123.5.\\; 3457000\\)</p>", "advice": "", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "siground(random(-200..200 #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>Round \\(\\var{a}\\) to \\(3\\) significant figures.</p>\n<p>Answer: [[0]]</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "siground(a,3)", "maxValue": "siground(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/"}]}