// Numbas version: exam_results_page_options
{"name": "Rounding: to a given number of significant figures", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Rounding: to a given number of significant figures", "tags": ["rounding"], "metadata": {"description": "<p>Round numbers to&nbsp;a given number of&nbsp;significant figures.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "<p>The&nbsp;first&nbsp;thing to do&nbsp;when we are rounding numbers is to identify the last digit we are keeping.</p>\n<p>When you're asked to <strong>round</strong> your answer to a number of significant figures, you need to decide whether to keep the last&nbsp;digit same (rounding down) or increase it by 1 (rounding up). If the following digit is less than 5 we round down and we round up&nbsp;when the next digit is 5 or more.</p>\n<p>To write it down in steps:</p>\n<ol>\n<ol>\n<ol>\n<ol>\n<li style=\"text-align: left;\">Identify the last digit we need to keep.</li>\n<li style=\"text-align: left;\">Look at the following digit.</li>\n<li style=\"text-align: left;\">If it's 5 or more, increase the previous digit by one.</li>\n<li class=\"c-list__ordered-item\" style=\"text-align: left;\">If it's 4 or less, keep the previous digit the same.</li>\n<li class=\"c-list__ordered-item\" style=\"text-align: left;\">Fill any spaces to the right of the digit with zeros if needed.</li>\n</ol>\n</ol>\n</ol>\n</ol>\n<p class=\"c-list__ordered-item\">It is important to keep in mind that if the digit we are increasing is 9, it becomes zero and we increase the previous digit instead. If this digit is 9 as well, we&nbsp;move along&nbsp;to the left side until we find a digit less than 9.</p>\n<p class=\"c-list__ordered-item\">The last digit we need to keep will depend on how many zeros there are. &nbsp;We don't consider leading zeros to be significant, <br/>i.e.&nbsp;0.03 and 0.3 both have 1 significant figure (but 0.30 has two significant figures, since the second zero isn't a 'leading' zero).</p>\n<h4 class=\"c-list__ordered-item\">a)</h4>\n<p><em>i)</em></p>\n<p style=\"padding-left: 30px;\">We round $\\var{d1}$ to&nbsp;1 significant figure. The first non-zero digit is $\\var{ddig[5]}$. The following digit is $\\var{ddig[4]}$ so we round <span data-jme-visible=\"ddig[4] &gt; 4\">up</span><span data-jme-visible=\"ddig[4] &lt; 5\">down</span> to get $\\var{dpformat(siground(d1, 1), 0)}$.</p>\n<p><em>ii)</em></p>\n<p style=\"padding-left: 30px;\">We round $\\var{d1}$ to&nbsp;{sf} significant figures. The first non-zero digit is $\\var{ddig[5]}$. The second following digit is $\\var{ddig[4]}$<span data-jme-visible=\"sf &gt; 2\">, the third following digit is $\\var{ddig[3]}$</span><span data-jme-visible=\"sf = 4\"> and the fourth following digit is $\\var{ddig[2]}$</span>. The&nbsp;digit&nbsp;following the last digit we are keeping is&nbsp;<span data-jme-visible=\"sf = 2\"> $\\var{ddig[3]}$</span><span data-jme-visible=\"sf = 3\">$\\var{ddig[2]}$</span><span data-jme-visible=\"sf = 4\">$\\var{ddig[1]}$</span>, so we round to&nbsp;get $\\var{sigformat(d1, sf)}$. These are our {sf} significant figures.&nbsp;</p>\n<p><em></em></p>\n<h4>b)</h4>\n<p><em>i)</em></p>\n<p style=\"padding-left: 30px;\">We round $\\var{e1}$ to 1 significant figure. The first non-zero digit is $\\var{edig[4]}$, followed by $\\var{edig[3]}$. This is <span data-jme-visible=\"edig[3] &lt; 5\">lower than 5 so we round down</span><span data-jme-visible=\"edig[3] &gt; 4\">more than 5 so we round up</span> to get $\\var{sigformat(e1,1)}$.</p>\n<p><em>ii)</em></p>\n<p style=\"padding-left: 30px;\">We round $\\var{e1}$ to&nbsp;{sf} significant figures. The first non-zero digit is $\\var{edig[4]}$. The second following digit is $\\var{edig[3]}$<span data-jme-visible=\"sf &gt; 2\">, the third following digit is $\\var{edig[2]}$</span><span data-jme-visible=\"sf = 4\"> and the fourth following digit is $\\var{edig[1]}$</span>. The&nbsp;digit&nbsp;following the last digit we are keeping is <span data-jme-visible=\"sf = 2\">$\\var{edig[2]}$</span><span data-jme-visible=\"sf = 3\">$\\var{edig[1]}$</span><span data-jme-visible=\"sf = 4\">$\\var{edig[0]}$</span>, so we round to&nbsp;get $\\var{sigformat(e1, sf)}$. These are our {sf} significant figures.&nbsp;</p>\n<p style=\"padding-left: 30px;\"></p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"edig": {"name": "edig", "group": "Ungrouped variables", "definition": "repeat(random(1..9), 5)", "description": "", "templateType": "anything", "can_override": false}, "d1": {"name": "d1", "group": "Ungrouped variables", "definition": "n_from_digits(ddig)", "description": "<p>Random integer.</p>", "templateType": "anything", "can_override": false}, "e1": {"name": "e1", "group": "Ungrouped variables", "definition": "n_from_digits(edig)*10^(random(-6,-7,-8))", "description": "<p>Random number with&nbsp;7 decimal places.</p>", "templateType": "anything", "can_override": false}, "ddig": {"name": "ddig", "group": "Ungrouped variables", "definition": "repeat(random(1..9), 6)", "description": "", "templateType": "anything", "can_override": false}, "sf": {"name": "sf", "group": "Ungrouped variables", "definition": "3", "description": "<p>Number of significant figures to round.</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": "100"}, "ungrouped_variables": ["sf", "ddig", "edig", "d1", "e1"], "variable_groups": [], "functions": {"n_from_digits": {"parameters": [["digits", "list"]], "type": "number", "language": "jme", "definition": "if(\n  len(digits)=0,\n    0,\n    digits[0]+10*n_from_digits(digits[1..len(digits)])\n)"}}, "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 $\\var{d1}$&nbsp;</p>\n<p style=\"padding-left: 60px;\"><em>i) </em>$\\var{d1}$ rounded&nbsp;to 1 significant figure is:&nbsp; [[0]]</p>\n<p style=\"padding-left: 60px;\"><em>ii)</em> $\\var{d1}$ rounded&nbsp;to {sf} significant figures is:&nbsp; [[1]]</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": "precround(siground(d1, 1),0)", "maxValue": "precround(siground(d1, 1),0)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"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(d1, sf)", "maxValue": "siground(d1, sf)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "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>Round $\\var{e1}$</p>\n<p style=\"padding-left: 60px;\"><em>iii)</em> $\\var{e1}$ rounded&nbsp;to 1 significant figure is:&nbsp; [[0]]</p>\n<p style=\"padding-left: 60px;\"><em>iv)</em> $\\var{e1}$ rounded&nbsp;to {sf} significant figures is:&nbsp; [[1]]</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(e1, 1)", "maxValue": "siground(e1, 1)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"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(e1, sf)", "maxValue": "siground(e1, sf)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Stanislav Duris", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1590/"}, {"name": "Ruth Hand", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3228/"}]}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Stanislav Duris", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1590/"}, {"name": "Ruth Hand", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3228/"}]}