// Numbas version: exam_results_page_options {"name": "Scientific notation: scientific notation to small numbers", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Scientific notation: scientific notation to small numbers", "tags": ["converting", "scientific notation", "standard form"], "metadata": {"description": "

Convert numbers between 0 and 1 from standard form/scientific notation.

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

Write the following numbers in decimal notation.

Part a)

\n

Multiplying a number by $10^\\var{pow1}$ will move the digits $\\var{-pow1}$ places to the right to make the number smaller. This is because

\n

\$10^\\var{pow1}=\\frac{1}{10^\\var{-pow1}}=\\frac{1}{\\var{10^-pow1}}=\\var{10^pow1}\$

\n

and so multiplying by it must make the original number smaller. In particular,

\n

\$\\var{dec1}\\times 10^\\var{pow1}=\\var{q1}\$

\n

Note you should always put a zero in front of your decimal point.

\n

\n

Part b)

\n

Multiplying a number by $10^\\var{pow2}$ will move the digits $\\var{-pow2}$ places to the right, to make the number smaller. This is because

\n

\$10^\\var{pow2}=\\frac{1}{10^\\var{-pow2}}=\\frac{1}{\\var{10^-pow2}}=\\var{10^pow2}\$

\n

and so multiplying by it must make the original number smaller. In particular,

\n

\$\\var{dec2}\\times 10^\\var{pow2}=\\var{q2}\$

\n

Note you should always put a zero in front of your decimal point.

", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"q2": {"name": "q2", "group": "Ungrouped variables", "definition": "precround(dec2*10^pow2,14)", "description": "", "templateType": "anything", "can_override": false}, "q1": {"name": "q1", "group": "Ungrouped variables", "definition": "precround(dec1*10^pow1,14)", "description": "", "templateType": "anything", "can_override": false}, "pow2": {"name": "pow2", "group": "Ungrouped variables", "definition": "random(list(-6..-1) except pow1)", "description": "", "templateType": "anything", "can_override": false}, "dec1": {"name": "dec1", "group": "Ungrouped variables", "definition": "random(1.1..9.9#0.01)", "description": "", "templateType": "anything", "can_override": false}, "pow1": {"name": "pow1", "group": "Ungrouped variables", "definition": "random(-1..-6)", "description": "", "templateType": "anything", "can_override": false}, "dec2": {"name": "dec2", "group": "Ungrouped variables", "definition": "random(1.1..9.9#0.001)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["dec1", "pow1", "q1", "dec2", "pow2", "q2"], "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": "

$\\var{dec1}\\times 10^\\var{pow1}$ = [[0]]

", "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": "{q1}", "maxValue": "{q1}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "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": "

$\\var{dec2}\\times 10^\\var{pow2}$ = [[0]]

", "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": "{q2}", "maxValue": "{q2}", "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", "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"name": "Ruth Hand", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3228/"}]}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"name": "Ruth Hand", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3228/"}]}