// 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": [{"tags": ["converting", "scientific notation", "standard form"], "variablesTest": {"maxRuns": 100, "condition": ""}, "rulesets": {}, "extensions": [], "variable_groups": [], "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 decimal&nbsp;notation.</p>", "name": "Scientific notation: scientific notation to small numbers", "ungrouped_variables": ["dec1", "pow1", "q1", "dec2", "pow2", "q2"], "functions": {}, "preamble": {"js": "", "css": ""}, "advice": "", "variables": {"q2": {"definition": "precround(dec2*10^pow2,14)", "templateType": "anything", "group": "Ungrouped variables", "name": "q2", "description": ""}, "q1": {"definition": "precround(dec1*10^pow1,14)", "templateType": "anything", "group": "Ungrouped variables", "name": "q1", "description": ""}, "pow2": {"definition": "random(list(-6..-1) except pow1)", "templateType": "anything", "group": "Ungrouped variables", "name": "pow2", "description": ""}, "dec1": {"definition": "random(1.1..9.9#0.01)", "templateType": "anything", "group": "Ungrouped variables", "name": "dec1", "description": ""}, "pow1": {"definition": "random(-1..-6)", "templateType": "anything", "group": "Ungrouped variables", "name": "pow1", "description": ""}, "dec2": {"definition": "random(1.1..9.9#0.001)", "templateType": "anything", "group": "Ungrouped variables", "name": "dec2", "description": ""}}, "metadata": {"licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International", "description": ""}, "parts": [{"variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "type": "gapfill", "unitTests": [], "marks": 0, "variableReplacements": [], "gaps": [{"variableReplacementStrategy": "originalfirst", "correctAnswerStyle": "plain", "mustBeReduced": false, "showFeedbackIcon": true, "type": "numberentry", "mustBeReducedPC": 0, "allowFractions": false, "unitTests": [], "marks": 1, "variableReplacements": [], "showCorrectAnswer": true, "scripts": {}, "customMarkingAlgorithm": "", "notationStyles": ["plain", "en", "si-en"], "maxValue": "{q1}", "minValue": "{q1}", "correctAnswerFraction": false, "extendBaseMarkingAlgorithm": true}], "showCorrectAnswer": true, "scripts": {}, "customMarkingAlgorithm": "", "stepsPenalty": "1", "prompt": "<p>$\\var{dec1}\\times 10^\\var{pow1}$ =&nbsp;[[0]]</p>", "sortAnswers": false, "steps": [{"scripts": {}, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "type": "information", "customMarkingAlgorithm": "", "unitTests": [], "marks": 0, "variableReplacements": [], "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}\\]</p>\n<p>are both in scientific notation.</p>\n<p></p>\n<hr/>\n<p>Multiplying a number by $10^\\var{pow1}$ will move the decimal point&nbsp;$\\var{-pow1}$ place<span data-jme-visible=\"pow1&lt;&gt;-1\">s</span> to make the number smaller (the decimal point moves to the left). This is because</p>\n<p>\\[10^\\var{pow1}=\\frac{1}{10^\\var{-pow1}}=\\frac{1}{\\var{10^-pow1}}=\\var{10^pow1}\\]</p>\n<p>and so multiplying by it must make the original number smaller. In particular,</p>\n<p>\\[\\var{dec1}\\times 10^\\var{pow1}=\\var{q1}\\]</p>\n<p><em>Note you should always put a zero in front of your decimal point.</em></p>", "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true}], "extendBaseMarkingAlgorithm": true}, {"variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "type": "gapfill", "unitTests": [], "marks": 0, "variableReplacements": [], "gaps": [{"variableReplacementStrategy": "originalfirst", "correctAnswerStyle": "plain", "mustBeReduced": false, "showFeedbackIcon": true, "type": "numberentry", "mustBeReducedPC": 0, "allowFractions": false, "unitTests": [], "marks": 1, "variableReplacements": [], "showCorrectAnswer": true, "scripts": {}, "customMarkingAlgorithm": "", "notationStyles": ["plain", "en", "si-en"], "maxValue": "{q2}", "minValue": "{q2}", "correctAnswerFraction": false, "extendBaseMarkingAlgorithm": true}], "showCorrectAnswer": true, "scripts": {}, "customMarkingAlgorithm": "", "stepsPenalty": "1", "prompt": "<p>$\\var{dec2}\\times 10^\\var{pow2}$ =&nbsp;[[0]]</p>", "sortAnswers": false, "steps": [{"scripts": {}, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "type": "information", "customMarkingAlgorithm": "", "unitTests": [], "marks": 0, "variableReplacements": [], "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}\\]</p>\n<p>are both in scientific notation.</p>\n<p></p>\n<hr/>\n<p>Multiplying a number by $10^\\var{pow2}$ will move the decimal point&nbsp;$\\var{-pow2}$ place<span data-jme-visible=\"pow2&lt;&gt;-1\">s</span> to make the number smaller (the decimal point moves to the left). This is because</p>\n<p>\\[10^\\var{pow2}=\\frac{1}{10^\\var{-pow2}}=\\frac{1}{\\var{10^-pow2}}=\\var{10^pow2}\\]</p>\n<p>and so multiplying by it must make the original number smaller. In particular,</p>\n<p>\\[\\var{dec2}\\times 10^\\var{pow2}=\\var{q2}\\]</p>\n<p><em>Note you should always put a zero in front of your decimal point.</em></p>", "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true}], "extendBaseMarkingAlgorithm": true}], "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/"}]}