// Numbas version: finer_feedback_settings
{"name": "Scientific notation: small numbers to scientific notation", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Scientific notation: small numbers to scientific notation", "variables": {"pow2": {"definition": "random(list(-6..-1) except pow1)", "name": "pow2", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "dec2": {"definition": "random(1.1..9.9#0.001)", "name": "dec2", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "q1": {"definition": "precround(dec1*10^pow1,14)", "name": "q1", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "dec1": {"definition": "random(1.1..9.9#0.01)", "name": "dec1", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "q2": {"definition": "precround(dec2*10^pow2,14)", "name": "q2", "group": "Ungrouped variables", "description": "", "templateType": "anything"}, "pow1": {"definition": "random(-1..-6)", "name": "pow1", "group": "Ungrouped variables", "description": "", "templateType": "anything"}}, "ungrouped_variables": ["dec1", "pow1", "q1", "dec2", "pow2", "q2"], "extensions": [], "parts": [{"stepsPenalty": "1", "steps": [{"showCorrectAnswer": true, "scripts": {}, "customMarkingAlgorithm": "", "prompt": "<p>A number is in scientific notation if it is written as a decimal multiplied by some power of 10, where the decimal has exactly one digit in front of the decimal place. For example:</p>\n<p>\\[1.234\\times 10^6, \\quad \\text{and} \\quad 3.01\\times 10^{-3}\\]&nbsp;</p>\n<p>are both in scientific notation.</p>\n<hr/>\n<p>Suppose we have the number $\\var{q1}$. In scientific notation, this number would start with $\\var{dec1}$ since we only want one digit in front of the decimal point. The decimal point&nbsp;is&nbsp;currently here $\\var{q1}$ and needs to move to between the&nbsp;first and second digits, that is $\\var{dec1}$. Count the places that the decimal point must jump and you get $\\var{-pow1}$ places. That is,&nbsp;&nbsp;</p>\n<p></p>\n<p>\\[\\var{q1}=\\var{dec1}\\times 10^{\\var{pow1}}\\]</p>\n<p></p>\n<p>We have a <em>negative $\\var{-pow1}$</em>&nbsp;as the power because we need to make the number $\\var{dec1}$ <em>smaller</em> to get to $\\var{q1}$.</p>", "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "unitTests": [], "marks": 0, "showFeedbackIcon": true, "variableReplacements": [], "type": "information"}], "gaps": [{"notationStyles": ["plain", "en", "si-en"], "scripts": {}, "correctAnswerFraction": false, "marks": "0.5", "variableReplacementStrategy": "originalfirst", "allowFractions": false, "variableReplacements": [], "type": "numberentry", "showCorrectAnswer": false, "maxValue": "{dec1}", "mustBeReduced": false, "minValue": "{dec1}", "mustBeReducedPC": 0, "correctAnswerStyle": "plain", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showFeedbackIcon": true, "customMarkingAlgorithm": ""}, {"notationStyles": ["plain", "en", "si-en"], "scripts": {}, "correctAnswerFraction": false, "marks": "0.5", "variableReplacementStrategy": "originalfirst", "allowFractions": false, "variableReplacements": [], "type": "numberentry", "showCorrectAnswer": false, "maxValue": "{pow1}", "mustBeReduced": false, "minValue": "{pow1}", "mustBeReducedPC": 0, "correctAnswerStyle": "plain", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showFeedbackIcon": true, "customMarkingAlgorithm": ""}], "scripts": {}, "marks": 0, "sortAnswers": false, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "type": "gapfill", "showCorrectAnswer": true, "prompt": "<p>$\\var{q1}$ =&nbsp;[[0]]$\\times 10$&nbsp;<sup>[[1]]</sup></p>", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showFeedbackIcon": true, "customMarkingAlgorithm": ""}, {"stepsPenalty": "1", "steps": [{"showCorrectAnswer": true, "scripts": {}, "customMarkingAlgorithm": "", "prompt": "<p>A number is in scientific notation if it is written as a decimal multiplied by some power of 10, where the decimal has exactly one digit in front of the decimal place. For example:</p>\n<p>\\[1.234\\times 10^6, \\quad \\text{and} \\quad 3.01\\times 10^{-3}\\]&nbsp;</p>\n<p>are both in scientific notation.</p>\n<hr/>\n<p>Suppose we have the number $\\var{q2}$. In scientific notation, this number would start with $\\var{dec2}$ since we only want one digit in front of the decimal point.&nbsp;The decimal point&nbsp;is&nbsp;currently here $\\var{q2}$ and needs to move to between the&nbsp;first and second digits, that is $\\var{dec2}$. Count the places that the decimal point must jump and you get $\\var{-pow2}$ places. That is,&nbsp;&nbsp;</p>\n<p></p>\n<p>\\[\\var{q2}=\\var{dec2}\\times 10^{\\var{pow2}}\\]</p>\n<p></p>\n<p>We have a&nbsp;<em>negative&nbsp;$\\var{-pow2}$</em>&nbsp;as the power because we need to make the number $\\var{dec2}$&nbsp;<em>smaller</em>&nbsp;to get to $\\var{q2}$.</p>", "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "unitTests": [], "marks": 0, "showFeedbackIcon": true, "variableReplacements": [], "type": "information"}], "gaps": [{"notationStyles": ["plain", "en", "si-en"], "scripts": {}, "correctAnswerFraction": false, "marks": "0.5", "variableReplacementStrategy": "originalfirst", "allowFractions": false, "variableReplacements": [], "type": "numberentry", "showCorrectAnswer": false, "maxValue": "{dec2}", "mustBeReduced": false, "minValue": "{dec2}", "mustBeReducedPC": 0, "correctAnswerStyle": "plain", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showFeedbackIcon": true, "customMarkingAlgorithm": ""}, {"notationStyles": ["plain", "en", "si-en"], "scripts": {}, "correctAnswerFraction": false, "marks": "0.5", "variableReplacementStrategy": "originalfirst", "allowFractions": false, "variableReplacements": [], "type": "numberentry", "showCorrectAnswer": false, "maxValue": "{pow2}", "mustBeReduced": false, "minValue": "{pow2}", "mustBeReducedPC": 0, "correctAnswerStyle": "plain", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showFeedbackIcon": true, "customMarkingAlgorithm": ""}], "scripts": {}, "marks": 0, "sortAnswers": false, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "type": "gapfill", "showCorrectAnswer": true, "prompt": "<p>$\\var{q2}$ =&nbsp;[[0]]$\\times 10$&nbsp;<sup>[[1]]</sup></p>", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showFeedbackIcon": true, "customMarkingAlgorithm": ""}], "functions": {}, "rulesets": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "tags": ["converting", "scientific notation", "standard form"], "statement": "<p>If you are unsure of how to do&nbsp;a question, click on&nbsp;<em>Show steps</em>&nbsp;to see the full working. Then, once you understand how to do the question, click on&nbsp;<em>Try another question like this one</em>&nbsp;to start again.</p>\n<p></p>\n<p>Write the following numbers in scientific notation.</p>", "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "variable_groups": [], "preamble": {"js": "", "css": ""}, "advice": "", "type": "question", "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}