// Numbas version: exam_results_page_options {"name": "Decimal Places and Significant Figures", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Decimal Places and Significant Figures", "tags": ["decimal", "rebel", "REBEL", "Rebel", "rebelmaths", "significant"], "metadata": {"description": "

Decimal Places and Significant Figures

\n

rebelmaths

", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "

Evaluate each of the following:

", "advice": "

When rounding to a given number of decimal places

\n

When rounding to a given number of decimal places, do the following

\n

Look at the next number after the last number of the decimal places you need to round to

\n

If the number is 5 or greater, round up, if it is than 5, leave as is; i.e.

\n

round to 3 decimal places the following

\n

$0.0055 = 0.006$

\n

$0.0071 = 0.007$

\n

\n

When rounding to a given number of significant figures

\n

When rounding to a given number of significant figures, do the following

\n

Look at the next number after the last number of the significant figuresyou need to round to

\n

If the number is 5 or greater, round up, if it is than 5, leave as is; i.e.

\n

N.B. Remember to keep the number you rounded to the significant number of places in the same unit e.g. 10's, 100's etc

\n

round to 3 significant figures the following

\n

$2573 = 2570$

\n

$7828 = 7830$

\n

round to 1 significant figures the following

\n

$15 = 20$

\n

$38851 = 40000$

", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"f1": {"name": "f1", "group": "Ungrouped variables", "definition": "random(0.0022..0.0049#0.0001) ", "description": "", "templateType": "anything", "can_override": false}, "f2": {"name": "f2", "group": "Ungrouped variables", "definition": "random(50000..100000#0.5)", "description": "", "templateType": "anything", "can_override": false}, "f3": {"name": "f3", "group": "Ungrouped variables", "definition": "f1*f2", "description": "", "templateType": "anything", "can_override": false}, "numa2": {"name": "numa2", "group": "Ungrouped variables", "definition": "random(0.11..0.19#0.01)", "description": "", "templateType": "anything", "can_override": false}, "numa1": {"name": "numa1", "group": "Ungrouped variables", "definition": "random(0.0011..0.0035)", "description": "", "templateType": "anything", "can_override": false}, "h2": {"name": "h2", "group": "Ungrouped variables", "definition": "random(1.225..1.975#0.05) ", "description": "", "templateType": "anything", "can_override": false}, "ans1": {"name": "ans1", "group": "Ungrouped variables", "definition": "numa1*numa2", "description": "", "templateType": "anything", "can_override": false}, "ans2": {"name": "ans2", "group": "Ungrouped variables", "definition": "numb1*numb2", "description": "", "templateType": "anything", "can_override": false}, "ans3": {"name": "ans3", "group": "Ungrouped variables", "definition": "numc1*numc2", "description": "", "templateType": "anything", "can_override": false}, "ans4": {"name": "ans4", "group": "Ungrouped variables", "definition": "numd1*numd2", "description": "", "templateType": "anything", "can_override": false}, "numc1": {"name": "numc1", "group": "Ungrouped variables", "definition": "random(1.2..1.4#0.01)", "description": "", "templateType": "anything", "can_override": false}, "numc2": {"name": "numc2", "group": "Ungrouped variables", "definition": "random(0.0011..0.0059#0.0001)", "description": "", "templateType": "anything", "can_override": false}, "d2": {"name": "d2", "group": "Ungrouped variables", "definition": "random(50.5..69.5#0.5)", "description": "", "templateType": "anything", "can_override": false}, "d3": {"name": "d3", "group": "Ungrouped variables", "definition": "d1*d2", "description": "", "templateType": "anything", "can_override": false}, "d1": {"name": "d1", "group": "Ungrouped variables", "definition": "random(0.2..0.8#0.1)", "description": "", "templateType": "anything", "can_override": false}, "sig": {"name": "sig", "group": "Ungrouped variables", "definition": "random(800..2000#0.0001) ", "description": "", "templateType": "anything", "can_override": false}, "h3": {"name": "h3", "group": "Ungrouped variables", "definition": "h1*h2", "description": "", "templateType": "anything", "can_override": false}, "numb2": {"name": "numb2", "group": "Ungrouped variables", "definition": "random(0.002..0.009#0.001)", "description": "", "templateType": "anything", "can_override": false}, "numb1": {"name": "numb1", "group": "Ungrouped variables", "definition": "random(0.000033..0.000079#0.000001)", "description": "", "templateType": "anything", "can_override": false}, "h1": {"name": "h1", "group": "Ungrouped variables", "definition": "random(0.0022..0.0055#0.000001) ", "description": "", "templateType": "anything", "can_override": false}, "g3": {"name": "g3", "group": "Ungrouped variables", "definition": "g1*g2", "description": "", "templateType": "anything", "can_override": false}, "g2": {"name": "g2", "group": "Ungrouped variables", "definition": "random(0.0022..0.0049#0.0001) ", "description": "", "templateType": "anything", "can_override": false}, "g1": {"name": "g1", "group": "Ungrouped variables", "definition": "random(21.1..31.1#0.2) ", "description": "", "templateType": "anything", "can_override": false}, "numd1": {"name": "numd1", "group": "Ungrouped variables", "definition": "random(20.1..91.1#0.2)", "description": "", "templateType": "anything", "can_override": false}, "numd2": {"name": "numd2", "group": "Ungrouped variables", "definition": "random(0.0201..0.0299#0.0002)", "description": "", "templateType": "anything", "can_override": false}, "e1": {"name": "e1", "group": "Ungrouped variables", "definition": "random(0.0002..0.0009)", "description": "", "templateType": "anything", "can_override": false}, "e3": {"name": "e3", "group": "Ungrouped variables", "definition": "e1*e2", "description": "", "templateType": "anything", "can_override": false}, "e2": {"name": "e2", "group": "Ungrouped variables", "definition": "random(50000..100000#0.5)", "description": "", "templateType": "anything", "can_override": false}, "dec": {"name": "dec", "group": "Ungrouped variables", "definition": "random(0.0001..0.0009#0.0000001) ", "description": "", "templateType": "anything", "can_override": false}, "rand2": {"name": "rand2", "group": "Ungrouped variables", "definition": "random(1..4 except {rand1})", "description": "", "templateType": "anything", "can_override": false}, "rand3": {"name": "rand3", "group": "Ungrouped variables", "definition": "rand()", "description": "", "templateType": "anything", "can_override": false}, "rand1": {"name": "rand1", "group": "Ungrouped variables", "definition": "rand()", "description": "", "templateType": "anything", "can_override": false}, "rand4": {"name": "rand4", "group": "Ungrouped variables", "definition": "random(1..4 except{rand3})", "description": "", "templateType": "anything", "can_override": false}, "rand5": {"name": "rand5", "group": "Ungrouped variables", "definition": "random(1..4 except {rand4} except{rand3})", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["numa1", "numa2", "numb1", "numb2", "ans1", "ans2", "numc1", "numc2", "ans3", "numd1", "numd2", "ans4", "d3", "d1", "d2", "e3", "e1", "e2", "f3", "f1", "f2", "g3", "g1", "g2", "h3", "h1", "h2", "sig", "dec", "rand1", "rand2", "rand3", "rand4", "rand5"], "variable_groups": [], "functions": {"rand": {"parameters": [], "type": "number", "language": "jme", "definition": "random(1..4)"}}, "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": "

Round off $\\var{sig}$ to:

\n

i)      2 decimal places   [[0]]

\n

ii)     1 decimal place   [[1]]

\n

iii)    3 significant figures      [[2]]

\n

iv)    2 significant figures      [[3]]

\n

v)     1 significant figure      [[4]]

", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{sig}", "maxValue": "{sig}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "2", "precisionPartialCredit": "0", "precisionMessage": "", "strictPrecision": true, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{sig}", "maxValue": "{sig}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "1", "precisionPartialCredit": 0, "precisionMessage": "", "strictPrecision": true, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{sig}", "maxValue": "{sig}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "sigfig", "precision": "3", "precisionPartialCredit": 0, "precisionMessage": "", "strictPrecision": true, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{sig}", "maxValue": "{sig}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "sigfig", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "", "strictPrecision": true, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{sig}", "maxValue": "{sig}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "sigfig", "precision": "1", "precisionPartialCredit": 0, "precisionMessage": "", "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": "

Round off $\\var{dec}$ to:

\n

i)      4 decimal places   [[0]]

\n

ii)     5 decimal places   [[1]]

\n

iii)    3 significant figures     [[2]]

\n

iv)    2 significant figures      [[3]]

\n

v)     1 significant figure      [[4]]

", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{dec}", "maxValue": "{dec}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "4", "precisionPartialCredit": 0, "precisionMessage": "", "strictPrecision": true, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{dec}", "maxValue": "{dec}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "5", "precisionPartialCredit": "0", "precisionMessage": "", "strictPrecision": true, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{dec}", "maxValue": "{dec}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "sigfig", "precision": "3", "precisionPartialCredit": 0, "precisionMessage": "", "strictPrecision": true, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{dec}", "maxValue": "{dec}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "sigfig", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "", "strictPrecision": true, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{dec}", "maxValue": "{dec}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "sigfig", "precision": "1", "precisionPartialCredit": 0, "precisionMessage": "", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}, {"name": "Catherine Palmer", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/423/"}, {"name": "Patricia Cogan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3359/"}]}]}], "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}, {"name": "Catherine Palmer", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/423/"}, {"name": "Patricia Cogan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3359/"}]}