// Numbas version: exam_results_page_options
{"name": "Ugur's copy of Working with standard index form", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Ugur's copy of Working with standard index form", "type": "question", "statement": "<p>Working with numbers that are very large or very small can be tricky.</p>\n<p>Standard form allows us to simplify these numbers, using powers of 10.</p>\n<div style=\"text-align: left;\">The standard index form can be defined as</div>\n<div>\\[A&nbsp;\\times 10^n,\\]</div>\n<div>where $1 &le; A &lt; 10$ and $n$&nbsp;is an integer, e.g. $2.26 \\times 10^5$ is a standard form of a number 226000.</div>\n<div>\n<p>&nbsp;</p>\n<p>Write&nbsp;the following in standard index form (for example, for&nbsp;$2.01\\times 10^5$ we would write <code>2.01*10^5</code> in the gap).</p>\n</div>", "variablesTest": {"condition": "", "maxRuns": 100}, "variables": {"int": {"group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "int", "definition": "random(2..9)"}, "A3dp": {"group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "A3dp", "definition": "random(1..10 #0.001)"}, "B": {"group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "B", "definition": "repeat(random(3..9 #0.01), 4)"}, "small5": {"group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "small5", "definition": "random(0.00001..0.0001 #0.00000001)"}, "A5dp": {"group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "A5dp", "definition": "random(1..10 #0.00001)"}, "ran": {"group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "ran", "definition": "random([6,7,8,9,10])"}, "A": {"group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "A", "definition": "repeat(random(1..10 #0.01 except 10), 3)"}}, "extensions": [], "functions": {}, "tags": ["conversion", "converting", "standard form", "standard index form", "taxonomy"], "variable_groups": [], "parts": [{"scripts": {}, "variableReplacements": [], "marks": 0, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "gaps": [{"checkingtype": "absdiff", "scripts": {}, "showpreview": true, "variableReplacementStrategy": "originalfirst", "vsetrangepoints": 5, "showCorrectAnswer": true, "showFeedbackIcon": true, "answersimplification": "!collectnumbers", "checkingaccuracy": 0.001, "expectedvariablenames": [], "marks": "1", "notallowed": {"message": "", "partialCredit": 0, "showStrings": false, "strings": ["^-2", "^(-2)"]}, "vsetrange": [0, 1], "musthave": {"message": "", "partialCredit": 0, "showStrings": false, "strings": ["*10^2"]}, "variableReplacements": [], "answer": "{A[2]}*10^2", "checkvariablenames": false, "type": "jme"}], "showCorrectAnswer": true, "prompt": "<p style=\"padding-left: 30px;\">$\\var{A[2]*10^2} = $&nbsp; [[0]]</p>", "type": "gapfill"}, {"scripts": {}, "variableReplacements": [], "marks": 0, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "gaps": [{"checkingtype": "absdiff", "scripts": {}, "showpreview": true, "variableReplacementStrategy": "originalfirst", "vsetrangepoints": 5, "showCorrectAnswer": true, "showFeedbackIcon": true, "answersimplification": "!collectnumbers", "checkingaccuracy": 0.001, "expectedvariablenames": [], "marks": "1", "notallowed": {"message": "", "partialCredit": 0, "showStrings": false, "strings": ["*10^1"]}, "vsetrange": [0, 1], "musthave": {"message": "", "partialCredit": 0, "showStrings": false, "strings": ["*10^", "-1"]}, "variableReplacements": [], "answer": "{A3dp}*10^(-1)", "checkvariablenames": false, "type": "jme"}], "showCorrectAnswer": true, "prompt": "<p style=\"padding-left: 30px;\">$\\var{A3dp*10^(-1)} = $&nbsp; [[0]]</p>", "type": "gapfill"}, {"scripts": {}, "variableReplacements": [], "marks": 0, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "gaps": [{"checkingtype": "absdiff", "scripts": {}, "showpreview": true, "variableReplacementStrategy": "originalfirst", "vsetrangepoints": 5, "showCorrectAnswer": true, "showFeedbackIcon": true, "answersimplification": "!collectnumbers", "checkingaccuracy": 0.001, "expectedvariablenames": [], "marks": "1", "notallowed": {"message": "", "partialCredit": 0, "showStrings": false, "strings": ["^-7", "^(-7)"]}, "vsetrange": [0, 1], "musthave": {"message": "", "partialCredit": 0, "showStrings": false, "strings": ["*10^7"]}, "variableReplacements": [], "answer": "{A5dp}*10^7", "checkvariablenames": false, "type": "jme"}], "showCorrectAnswer": true, "prompt": "<p style=\"padding-left: 30px;\">$\\var{precround(A5dp*10^7,0)} =$&nbsp; [[0]]</p>", "type": "gapfill"}, {"scripts": {}, "variableReplacements": [], "marks": 0, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "gaps": [{"checkingtype": "absdiff", "scripts": {}, "showpreview": true, "variableReplacementStrategy": "originalfirst", "vsetrangepoints": 5, "showCorrectAnswer": true, "showFeedbackIcon": true, "answersimplification": "!collectnumbers", "checkingaccuracy": 0.001, "expectedvariablenames": [], "marks": "1", "notallowed": {"message": "", "partialCredit": 0, "showStrings": false, "strings": ["10^5"]}, "vsetrange": [0, 1], "musthave": {"message": "", "partialCredit": 0, "showStrings": false, "strings": ["*10^", "-5"]}, "variableReplacements": [], "answer": "{{small5}*10^5}*10^(-5)", "checkvariablenames": false, "type": "jme"}], "showCorrectAnswer": true, "prompt": "<p style=\"padding-left: 30px;\">$\\var{small5} = $&nbsp; [[0]]</p>", "type": "gapfill"}], "ungrouped_variables": ["A3dp", "A5dp", "small5", "A", "ran", "B", "int"], "rulesets": {}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Convert a variety of numbers from decimal to&nbsp;standard index form.</p>"}, "preamble": {"css": "", "js": ""}, "advice": "<p>Converting from decimal to a standard form, we are looking for $A&nbsp;\\times 10^n$.</p>\n<p>We need make the first number ($A$) between 1 and 10, so we put the decimal place after the first non-zero digit.</p>\n<p>&nbsp;</p>\n<p><strong>a)</strong></p>\n<p>In $\\var{A[2]*10^2}$, the first non-zero digit is $\\var{siground(A[2] - 0.5, 1)}$ so we get $A = \\var{A[2]}$.</p>\n<p style=\"padding-left: 30px;\">If we moved the decimal place&nbsp;in $\\var{A[2]}$ so it matches our original number $\\var{A[2]*10^2}$, we would go 2&nbsp;places to the right, so $n = 2$.</p>\n<p style=\"padding-left: 30px;\">&nbsp; </p>\n<p><strong>b)</strong></p>\n<p>In $\\var{A3dp*10^(-1)}$, the first non-zero digit is $\\var{siground(A3dp - 0.5, 1)}$ so we get&nbsp;$A = \\var{A3dp}$.</p>\n<p style=\"padding-left: 30px;\">If we moved the decimal place&nbsp;in $\\var{A3dp}$ so it matches our original number $\\var{A3dp*10^(-1)}$, we would go&nbsp;1&nbsp;place to the left, so $n = -1$.</p>\n<p style=\"padding-left: 30px;\">&nbsp; </p>\n<p><strong>c)</strong></p>\n<p>In $\\var{precround(A5dp*10^7,0)}$ the first non-zero digit is $\\var{siground(A5dp - 0.5, 1)}$ so we get $A = \\var{A5dp}$.</p>\n<p style=\"padding-left: 30px;\">If we moved the decimal place&nbsp;in $\\var{A5dp}$ so it matches our original number $\\var{precround(A5dp*10^7,0)}$, we would go&nbsp;7&nbsp;places to the right, so $n = 7$.</p>\n<p style=\"padding-left: 30px;\">&nbsp; </p>\n<h4>d)</h4>\n<p>In $\\var{small5}$ the first non-zero digit is {siground({{small5}*10^5} - 0.5, 1)} so we get $A = \\var{small5*10^5}$.</p>\n<p style=\"padding-left: 30px;\">If we moved the decimal place&nbsp;in $\\var{small5*10^5}$ so it matches our original number $\\var{small5}$, we would go&nbsp;5 places to the left, so $n = -5$.</p>\n<p style=\"padding-left: 30px;\"></p>", "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": "Ugur Efem", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/14200/"}]}]}], "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": "Ugur Efem", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/14200/"}]}