// Numbas version: exam_results_page_options
{"name": "1.2.6. Scientific Notation", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "1.2.6. Scientific Notation", "tags": [], "metadata": {"description": "<p>Part of HELM Book 1.2</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<h2>Scientific Notation</h2>\n<p>It is often necessary to use very large or very small numbers such as $78000000$ and $0.00000034$.<br/>Scientific notation can be used to express such numbers in a more concise form. Each number is written in the form</p>\n<p style=\"text-align: center;\">\\( a \\times 10^n \\)</p>\n<p>where $a$ is a number between $1$ and $10$. We can make use of the following facts:</p>\n<p style=\"text-align: center;\">$10 = 10^1$; $\\quad 100 = 10^2$; $\\quad 1000 = 10^3\\quad$ and so on</p>\n<p>and</p>\n<p style=\"text-align: center;\">$0.1 = 10^{-1}$; $\\quad 0.01 = 10^{-2}$; $\\quad 0.001 = 10^{-3}\\quad$ and so on.</p>\n<p>For example,</p>\n<ul>\n<li style=\"text-align: left;\">the number $5000$ can be written $5 \\times 1000 = 5 \\times 10^3$</li>\n<li style=\"text-align: left;\">the number $403$ can be written $4.03 \\times 100 = 4.03 \\times 10^2$</li>\n<li style=\"text-align: left;\">the number $0.009$ can be written $9 \\times 0.001 = 9 \\times 10^{-3}$</li>\n</ul>\n<p>Furthermore, to multiply a number by $10^n$ the decimal point is moved $n$ places to the right if $n$ is a positive integer, and $n$ places to the left if $n$ is a negative integer. (If necessary additional zeros are inserted to make up the required number of digits before the decimal point.)</p>", "advice": "", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"q1base": {"name": "q1base", "group": "Ungrouped variables", "definition": "decimal(random(10001..99999)/10000)", "description": "", "templateType": "anything", "can_override": false}, "q1expr": {"name": "q1expr", "group": "Ungrouped variables", "definition": "q1base*10^q1Idx", "description": "", "templateType": "anything", "can_override": false}, "q1idx": {"name": "q1idx", "group": "Ungrouped variables", "definition": "random(-7..7 except [-1,0,1])", "description": "", "templateType": "anything", "can_override": false}, "q2base": {"name": "q2base", "group": "Ungrouped variables", "definition": "eval(expression(split_regex(q2ans,\"e\")[0]))", "description": "", "templateType": "anything", "can_override": false}, "q2idx": {"name": "q2idx", "group": "Ungrouped variables", "definition": "eval(expression(split_regex(q2ans,\"e\")[1]))", "description": "", "templateType": "anything", "can_override": false}, "q2b1": {"name": "q2b1", "group": "Ungrouped variables", "definition": "decimal(random(11..99)/10)", "description": "", "templateType": "anything", "can_override": false}, "q2b2": {"name": "q2b2", "group": "Ungrouped variables", "definition": "decimal(random(11..99)/10)", "description": "", "templateType": "anything", "can_override": false}, "q2i1": {"name": "q2i1", "group": "Ungrouped variables", "definition": "random(-39..39 except [-1,0,1])", "description": "", "templateType": "anything", "can_override": false}, "q2i2": {"name": "q2i2", "group": "Ungrouped variables", "definition": "random(-39..39 except [-1,0,1])", "description": "", "templateType": "anything", "can_override": false}, "q2ans": {"name": "q2ans", "group": "Ungrouped variables", "definition": "formatnumber(eval(q2expr),\"scientific\")", "description": "", "templateType": "anything", "can_override": false}, "q2expr": {"name": "q2expr", "group": "Ungrouped variables", "definition": "expression(+q2b1 + \"* 10^(\" + q2i1 + \")*\" + q2b2 + \"* 10^(\" + q2i2 + \")\")", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["q1base", "q1idx", "q1expr", "q2b1", "q2b2", "q2i1", "q2i2", "q2expr", "q2base", "q2idx", "q2ans"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Task 1", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Write $\\var{q1Expr}$ in scientific notation:</p>\n<p>[[0]]$\\times 10$<sup>[[1]]</sup></p>", "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "q1Base", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{q1Base}", "maxValue": "{q1Base}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "q1Idx", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{q1Idx}", "maxValue": "{q1Idx}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "information", "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": "<h3>Engineering constants</h3>\n<p>Many constants appearing in engineering calculations are expressed in scientific notation. For example the charge on an electron equals $1.6 \\times 10^{-19}$ coulomb and the speed of light is $3 \\times 10^8$ m s$^{-1}$. Avogadro's constant is equal to $6.02 \\times 10^{23}$ and is the number of atoms in one mole of an element. Clearly the use of scientific notation avoids writing lengthy strings of zeros.</p>\n<p>Your scientific calculator will be able to accept numbers in scientific notation. Often the $E$ button (sometimes the $EXP$ button) is used and a number like $4.2\\times10^7$ will be entered as $4.2E7$. Note that $10E4$ means $10\\times 10^4$, that is, $10^5$. To enter the number $10^3$, say, you would key in $1E3$. Entering powers of $10$ incorrectly is a common cause of error. You must check how your particular calculator accepts numbers in scientific notation.</p>\n<p>The following task is designed to check that you can enter numbers given in scientific notation into your calculator.</p>"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}]}]}], "contributors": [{"name": "Merryn Horrocks", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4052/"}]}