// Numbas version: finer_feedback_settings
{"name": "Significant figures: rounding", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Significant figures: rounding", "tags": [], "metadata": {"description": "<p>Rounding integers and decimals to a specific number of sig figs.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Round the following numbers to the indicated precision.</p>", "advice": "<p>When rounding, we look at the first digit that we might discard. If it is $5$ or greater, we round up. If it is less than $5$, we round down.</p>\n<p></p>\n<p>a) To round to two significant figures, we look at the third significant figure to decide whether to round up or down.&nbsp;</p>\n<p>Since the third significant figure of $\\var{integer}$ is $\\var{thirddigit}$, we round $\\var{integer}$ <span data-jme-visible=\"thirddigit&gt;=5\">up</span> <span data-jme-visible=\"thirddigit&lt;5\">down</span> to $\\var{siground(integer,2)}$.</p>\n<p><span data-jme-visible=\"mod(integer,100)&lt;&gt;50\"> Note that $\\var{integer}$ is closer to $\\var{siground(integer,2)}$ than $\\var{wrongint}$.</span>&nbsp;</p>\n<p>b) To round to three significant figures, we look at the fourth significant figure to decide whether to round up or down.</p>\n<p>Since the fourth significant figure of $\\var{decimal}$ is $\\var{fourthdigit}$, we round $\\var{decimal}$ <span data-jme-visible=\"fourthdigit&gt;=5\">up</span> <span data-jme-visible=\"fourthdigit&lt;5\">down</span> to $\\var{siground(decimal,3)}$.&nbsp;</p>\n<p><span data-jme-visible=\"mod(decimal*10000,100)&lt;&gt;50\">Note that $\\var{decimal}$ is closer to $\\var{siground(decimal,3)}$ than $\\var{wrongdec}$.&nbsp;</span></p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"integer": {"name": "integer", "group": "Ungrouped variables", "definition": "random(1000..9999)", "description": "", "templateType": "anything", "can_override": false}, "decimal": {"name": "decimal", "group": "Ungrouped variables", "definition": "precround(random(1.11..9.99#0.01)+random(0.0051..0.0091#0.0001),4)", "description": "", "templateType": "anything", "can_override": false}, "thirddigit": {"name": "thirddigit", "group": "Ungrouped variables", "definition": "mod(trunc(integer/10,0),10)", "description": "", "templateType": "anything", "can_override": false}, "fourthdigit": {"name": "fourthdigit", "group": "Ungrouped variables", "definition": "mod(trunc(decimal*1000,0),10)", "description": "", "templateType": "anything", "can_override": false}, "wrongint": {"name": "wrongint", "group": "Ungrouped variables", "definition": "if(thirddigit>=5,trunc(integer,-2),trunc(integer,-2)+100)", "description": "", "templateType": "anything", "can_override": false}, "test": {"name": "test", "group": "Ungrouped variables", "definition": "trunc(4512.3,0)", "description": "", "templateType": "anything", "can_override": false}, "wrongdec": {"name": "wrongdec", "group": "Ungrouped variables", "definition": "if(fourthdigit>=5,trunc(decimal,2),trunc(decimal,2)+0.01)", "description": "", "templateType": "anything", "can_override": false}, "testy": {"name": "testy", "group": "Ungrouped variables", "definition": "mod(decimal*10000,100)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["integer", "decimal", "thirddigit", "fourthdigit", "wrongint", "test", "wrongdec", "testy"], "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 number {integer} rounded to two significant figures is&nbsp;[[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": "{integer}", "maxValue": "{integer}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "sigfig", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "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 number {decimal} rounded to three significant figures is&nbsp;[[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": "{decimal}", "maxValue": "{decimal}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "sigfig", "precision": "3", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "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/"}], "resources": []}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}