// Numbas version: finer_feedback_settings
{"name": "32. Calculations in standard form", "metadata": {"description": "<p>Performing calculations with numbers in standard form</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "duration": 0, "percentPass": 0, "showQuestionGroupNames": false, "shuffleQuestionGroups": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", "", ""], "variable_overrides": [[], [], [], []], "questions": [{"name": "32.a Multiplying standard form", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "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/"}, {"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}, {"name": "Will Morgan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21933/"}], "tags": ["converting", "scientific notation", "standard form"], "metadata": {"description": "<p>Convert numbers between 0 and 1 intro standard form/scientific notation.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Calculate the following expression and write the answer in standard form.</p>", "advice": "<p>To calculate $\\var{Num1}\\times 10^\\var{Pow1}\\times\\var{Num2}\\times 10^\\var{Pow2}$ we just multiply through and convert to standard form at the end if necessary. It is easier to multiply $\\var{Num1}$ with $\\var{Num2}$ and $10^\\var{Pow1}$ with $10^\\var{Pow2}$ which gives us</p>\n<p>\\[\\var{Num1}\\times 10^\\var{Pow1}\\times\\var{Num2}\\times 10^\\var{Pow2}=\\var{Num1*Num2}\\times10^\\var{Pow1+Pow2}.\\]</p>\n<p>{advice}</p>\n<p><a href=\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Standard\"><span style=\"font-weight: 400;\">Use this link to find some resources which will help you revise this topic.</span></a></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"PowAns": {"name": "PowAns", "group": "Ungrouped variables", "definition": "if(ChangePower, Pow1+Pow2+1, Pow1+Pow2)", "description": "", "templateType": "anything", "can_override": false}, "NumAns": {"name": "NumAns", "group": "Ungrouped variables", "definition": "dec(if(ChangePower, Num1*Num2/10, Num1*Num2))", "description": "", "templateType": "anything", "can_override": false}, "Num1": {"name": "Num1", "group": "Ungrouped variables", "definition": "random(1..9)", "description": "", "templateType": "anything", "can_override": false}, "Num2": {"name": "Num2", "group": "Ungrouped variables", "definition": "random(1..9)", "description": "", "templateType": "anything", "can_override": false}, "Pow1": {"name": "Pow1", "group": "Ungrouped variables", "definition": "random(-12..12)", "description": "", "templateType": "anything", "can_override": false}, "Pow2": {"name": "Pow2", "group": "Ungrouped variables", "definition": "random(-12..12)", "description": "", "templateType": "anything", "can_override": false}, "ChangePower": {"name": "ChangePower", "group": "Ungrouped variables", "definition": "Num1*Num2>=10", "description": "", "templateType": "anything", "can_override": false}, "Advice": {"name": "Advice", "group": "Ungrouped variables", "definition": "if(ChangePower, AdviceChangePower, AdviceNoChange)", "description": "", "templateType": "anything", "can_override": false}, "AdviceChangePower": {"name": "AdviceChangePower", "group": "Ungrouped variables", "definition": "\"<p>This is not in standard form, we need to divide $\\\\var{Num1*Num2}$ by $10$ and increase the power by $1$ to get a final answer of</p>\\n<p>\\\\[\\\\var{NumAns}\\\\times 10^\\\\var{PowAns}.\\\\]</p>\"", "description": "", "templateType": "long string", "can_override": false}, "AdviceNoChange": {"name": "AdviceNoChange", "group": "Ungrouped variables", "definition": "\"<p>Since this is already in standard form we are done.</p>\"", "description": "", "templateType": "long string", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["NumAns", "PowAns", "Num1", "Num2", "Pow1", "Pow2", "ChangePower", "Advice", "AdviceChangePower", "AdviceNoChange"], "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": "<p>$\\var{Num1}\\times 10^\\var{Pow1}\\times\\var{Num2}\\times 10^\\var{Pow2}=$ [[0]]$\\times 10$&nbsp;<sup>[[1]]&nbsp;</sup>.</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{NumAns}", "maxValue": "{NumAns}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{PowAns}", "maxValue": "{PowAns}", "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"}, {"name": "32.b Division in standard form", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "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/"}, {"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}, {"name": "Will Morgan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21933/"}], "tags": ["converting", "scientific notation", "standard form"], "metadata": {"description": "<p>Convert numbers between 0 and 1 intro standard form/scientific notation.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Calculate the following expression and write the answer in standard form.</p>", "advice": "<p>{advice}</p>\n<p><a href=\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Standard\"><span style=\"font-weight: 400;\">Use this link to find some resources which will help you revise this topic.</span></a></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"PowAns": {"name": "PowAns", "group": "Ungrouped variables", "definition": "if(ChangePower, Pow1-Pow2-1, Pow1-Pow2)", "description": "", "templateType": "anything", "can_override": false}, "NumAns": {"name": "NumAns", "group": "Ungrouped variables", "definition": "random(1..9)", "description": "", "templateType": "anything", "can_override": false}, "Num1": {"name": "Num1", "group": "Ungrouped variables", "definition": "if(DivdNum>=10, DivdNum*0.1, DivdNum)", "description": "", "templateType": "anything", "can_override": false}, "Num2": {"name": "Num2", "group": "Ungrouped variables", "definition": "random(1..9)", "description": "", "templateType": "anything", "can_override": false}, "Pow1": {"name": "Pow1", "group": "Ungrouped variables", "definition": "random(-12..12)", "description": "", "templateType": "anything", "can_override": false}, "Pow2": {"name": "Pow2", "group": "Ungrouped variables", "definition": "random(-12..12)", "description": "", "templateType": "anything", "can_override": false}, "ChangePower": {"name": "ChangePower", "group": "Ungrouped variables", "definition": "DivdNum>=10", "description": "", "templateType": "anything", "can_override": false}, "Advice": {"name": "Advice", "group": "Ungrouped variables", "definition": "if(ChangePower, AdviceChangePower, AdviceNoChange)", "description": "", "templateType": "anything", "can_override": false}, "AdviceChangePower": {"name": "AdviceChangePower", "group": "Ungrouped variables", "definition": "\"<p>It is easiest to think of</p>\\n<p>\\\\[\\\\left(\\\\var{Num1}\\\\times 10^\\\\var{Pow1}\\\\right)\\\\div\\\\left(\\\\var{Num2}\\\\times 10^\\\\var{Pow2}\\\\right)\\\\]</p>\\n<p>as the fraction</p>\\n<p>\\\\[\\\\frac{\\\\var{Num1}\\\\times 10^\\\\var{Pow1}}{\\\\var{Num2}\\\\times 10^\\\\var{Pow2}}\\\\]</p>\\n<p>at which point there are different ways to cancel down to one number in standard form. One option is to convert both numbers out of standard form but this can often be very messy. Alternatively we can simply divide $\\\\var{Num1}$ by $\\\\var{Num2}$ and $10^\\\\var{Pow1}$ by $10^\\\\var{Pow2}$ which gives us</p>\\n<p>\\\\[\\\\frac{\\\\var{Num1}\\\\times 10^\\\\var{Pow1}}{\\\\var{Num2}\\\\times 10^\\\\var{Pow2}}=\\\\var{Num1/Num2}\\\\times 10^\\\\var{Pow1-Pow2}.\\\\]</p>\\n<p>Since this is not in standard form we need to decrease the power by $1$ and multiply the number in front by $10$ to get a final answer of&nbsp;</p>\\n<p>\\\\[\\\\var{Num1/Num2*10}\\\\times 10^\\\\var{Pow1-Pow2-1}.\\\\]</p>\\n<p></p>\\n<p>Another option if you are not comfortable with dividing $\\\\var{Num1}$ by $\\\\var{Num2}$ is to multiply $\\\\var{Num1}$ by $10$ and decrease the power $\\\\var{Pow1}$ by $1$. This makes the division slightly easier as we get</p>\\n<p>\\\\[\\\\frac{\\\\var{Num1}\\\\times 10^\\\\var{Pow1}}{\\\\var{Num2}\\\\times 10^\\\\var{Pow2}}=\\\\frac{\\\\var{Num1*10}\\\\times 10^\\\\var{Pow1-1}}{\\\\var{Num2}\\\\times 10^\\\\var{Pow2}}=\\\\var{Num1/Num2*10}\\\\times10^\\\\var{Pow1-Pow2-1}.\\\\]</p>\\n<p>This is already in standard form so we are done.</p>\"", "description": "", "templateType": "long string", "can_override": false}, "AdviceNoChange": {"name": "AdviceNoChange", "group": "Ungrouped variables", "definition": "\"<p>It is easiest to think of</p>\\n<p>\\\\[\\\\left(\\\\var{Num1}\\\\times 10^\\\\var{Pow1}\\\\right)\\\\div\\\\left(\\\\var{Num2}\\\\times 10^\\\\var{Pow2}\\\\right)\\\\]</p>\\n<p>as the fraction</p>\\n<p>\\\\[\\\\frac{\\\\var{Num1}\\\\times 10^\\\\var{Pow1}}{\\\\var{Num2}\\\\times 10^\\\\var{Pow2}}\\\\]</p>\\n<p>and then we can cancel the terms which are easiest to divide. In this case it is easiest to divide $\\\\var{Num1}$ by $\\\\var{Num2}$ and $10^\\\\var{Pow1}$ by $10^\\\\var{Pow2}$ which gives us</p>\\n<p>\\\\[\\\\frac{\\\\var{Num1}\\\\times 10^\\\\var{Pow1}}{\\\\var{Num2}\\\\times 10^\\\\var{Pow2}}=\\\\var{Num1/Num2}\\\\times 10^\\\\var{Pow1-Pow2}.\\\\]</p>\\n<p>Since this is already in standard form then we are done.</p>\"", "description": "", "templateType": "long string", "can_override": false}, "DivdNum": {"name": "DivdNum", "group": "Ungrouped variables", "definition": "NumAns*Num2", "description": "<p>Number to divide by Num2 - not written in standard form.</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["NumAns", "PowAns", "Num1", "DivdNum", "Num2", "Pow1", "Pow2", "ChangePower", "Advice", "AdviceChangePower", "AdviceNoChange"], "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": "<p>$\\left(\\var{Num1}\\times 10^\\var{Pow1}\\right)\\div\\left(\\var{Num2}\\times 10^\\var{Pow2}\\right)=$ [[0]]$\\times 10$&nbsp;<sup>[[1]]&nbsp;</sup>.</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{NumAns}", "maxValue": "{NumAns}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{PowAns}", "maxValue": "{PowAns}", "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"}, {"name": "32.c Powers of standard form", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "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/"}, {"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}, {"name": "Will Morgan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21933/"}], "tags": ["converting", "scientific notation", "standard form"], "metadata": {"description": "<p>Convert numbers between 0 and 1 intro standard form/scientific notation.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Calculate the following expression and write the answer in standard form.</p>", "advice": "<p>To calculate</p>\n<p>\\[\\left(\\var{Num1}\\times 10^\\var{Pow1}\\right)^\\var{Pow2}\\]</p>\n<p>we simply expand the bracket to get</p>\n<p>\\[\\left(\\var{Num1}\\times 10^\\var{Pow1}\\right)^\\var{Pow2}\\]</p>\n<p>\\[=\\var{Num1}^\\var{Pow2}\\times \\left(10^\\var{Pow1}\\right)^\\var{Pow2}\\]</p>\n<p>\\[=\\var{Num1^Pow2}\\times 10^{\\var{Pow1}\\times\\var{Pow2}}\\]</p>\n<p>\\[=\\var{Num1^Pow2}\\times 10^{\\var{Pow1*Pow2}}\\]</p>\n<p>{advice}</p>\n<p><a href=\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Standard\"><span style=\"font-weight: 400;\">Use this link to find some resources which will help you revise this topic.</span></a></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"PowAns": {"name": "PowAns", "group": "Ungrouped variables", "definition": "Pow1*Pow2+PowerChange", "description": "", "templateType": "anything", "can_override": false}, "NumAns": {"name": "NumAns", "group": "Ungrouped variables", "definition": "Num1^Pow2*(10^-PowerChange)", "description": "", "templateType": "anything", "can_override": false}, "Num1": {"name": "Num1", "group": "Ungrouped variables", "definition": "random(1..5)", "description": "", "templateType": "anything", "can_override": false}, "Pow1": {"name": "Pow1", "group": "Ungrouped variables", "definition": "random(-12..12)", "description": "", "templateType": "anything", "can_override": false}, "Pow2": {"name": "Pow2", "group": "Ungrouped variables", "definition": "random(2..4)", "description": "", "templateType": "anything", "can_override": false}, "ChangePower": {"name": "ChangePower", "group": "Ungrouped variables", "definition": "Num1^Pow2>=10", "description": "", "templateType": "anything", "can_override": false}, "Advice": {"name": "Advice", "group": "Ungrouped variables", "definition": "if(ChangePower, AdviceChangePower, AdviceNoChange)", "description": "", "templateType": "anything", "can_override": false}, "AdviceChangePower": {"name": "AdviceChangePower", "group": "Ungrouped variables", "definition": "\"<p>This answer is not in standard form so we need to divide $\\\\var{Num1^Pow2}$ by $\\\\var{10^PowerChange}$ and increase the power $\\\\var{Pow1*Pow2}$ by $\\\\var{PowerChange}$ to get a final answer of</p>\\n<p>\\\\[\\\\var{NumAns}\\\\times10^\\\\var{PowAns}.\\\\]</p>\"", "description": "", "templateType": "long string", "can_override": false}, "AdviceNoChange": {"name": "AdviceNoChange", "group": "Ungrouped variables", "definition": "\"<p>Since this is already in standard form we are done.</p>\"", "description": "", "templateType": "long string", "can_override": false}, "PowerChange": {"name": "PowerChange", "group": "Ungrouped variables", "definition": "len(string(Num1^Pow2))-1", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["NumAns", "PowAns", "Num1", "Pow1", "Pow2", "ChangePower", "Advice", "AdviceChangePower", "AdviceNoChange", "PowerChange"], "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": "<p>$\\left(\\var{Num1}\\times 10^\\var{Pow1}\\right)^\\var{Pow2}=$ [[0]]$\\times 10$&nbsp;<sup>[[1]]&nbsp;</sup>.</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{NumAns}", "maxValue": "{NumAns}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{PowAns}", "maxValue": "{PowAns}", "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"}, {"name": "32.d Adding/Subtracting standard form", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "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/"}, {"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}, {"name": "Will Morgan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21933/"}], "tags": ["converting", "scientific notation", "standard form"], "metadata": {"description": "<p>Convert numbers between 0 and 1 intro standard form/scientific notation.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Calculate the following expression and write the answer in standard form.</p>", "advice": "<p>{advice}</p>\n<p><a href=\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Standard\"><span style=\"font-weight: 400;\">Use this link to find some resources which will help you revise this topic.</span></a></p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"PowAns": {"name": "PowAns", "group": "Ungrouped variables", "definition": "if(ChangePower, max(Pow1,Pow2)+1, max(Pow1,Pow2))", "description": "", "templateType": "anything", "can_override": false}, "NumAns": {"name": "NumAns", "group": "Ungrouped variables", "definition": "if(ChangePower, AddNums/10, AddNums)", "description": "", "templateType": "anything", "can_override": false}, "Num1": {"name": "Num1", "group": "Ungrouped variables", "definition": "random(1..9#0.1)", "description": "", "templateType": "anything", "can_override": false}, "Num2": {"name": "Num2", "group": "Ungrouped variables", "definition": "random(1..9#0.1)*random(-1,1)", "description": "", "templateType": "anything", "can_override": false}, "Pow1": {"name": "Pow1", "group": "Ungrouped variables", "definition": "random(-12..12)", "description": "", "templateType": "anything", "can_override": false}, "Pow2": {"name": "Pow2", "group": "Ungrouped variables", "definition": "Pow1+PowDiff", "description": "", "templateType": "anything", "can_override": false}, "ChangePower": {"name": "ChangePower", "group": "Ungrouped variables", "definition": "AddNums>=10", "description": "", "templateType": "anything", "can_override": false}, "Advice": {"name": "Advice", "group": "Advice", "definition": "if(PowDiff=0, AdviceSamePow,if(IsPow1Bigger, AdviceNum1Bigger, AdviceNum2Bigger))+if(ChangePower, AdviceChangePower, AdviceNoChange)", "description": "", "templateType": "anything", "can_override": false}, "AdviceChangePower": {"name": "AdviceChangePower", "group": "Advice", "definition": "\"<p>This is not in standard form, we need to divide $\\\\var{AddNums}$ by $10$ and increase the power by $1$ to get a final answer of</p>\\n<p>\\\\[\\\\var{NumAns}\\\\times 10^\\\\var{PowAns}.\\\\]</p>\"", "description": "", "templateType": "long string", "can_override": false}, "AdviceNoChange": {"name": "AdviceNoChange", "group": "Advice", "definition": "\"<p>Since this is already in standard form we are done.</p>\"", "description": "", "templateType": "long string", "can_override": false}, "PowDiff": {"name": "PowDiff", "group": "Ungrouped variables", "definition": "random(-2..2)", "description": "", "templateType": "anything", "can_override": false}, "IsPow1Bigger": {"name": "IsPow1Bigger", "group": "Ungrouped variables", "definition": "PowDiff<0", "description": "", "templateType": "anything", "can_override": false}, "AddNums": {"name": "AddNums", "group": "Ungrouped variables", "definition": "if(IsPow1Bigger, Num1+Num2*10^PowDiff, Num1*10^-PowDiff+Num2)", "description": "", "templateType": "anything", "can_override": false}, "AdviceNum1Bigger": {"name": "AdviceNum1Bigger", "group": "Advice", "definition": "\"<p>To add or subtract numbers in standard form we need both of the powers to be the same. We will write both numbers to the power&nbsp;of $\\\\var{Pow1}$. This gives us<br />\\\\[\\\\simplify[basic]{{Num1}*10^{Pow1}+{Num2}}\\\\times 10^\\\\var{Pow2}\\\\]</p>\\n<p>\\\\[=\\\\simplify[basic]{{Num1}*10^{Pow1}+{Num2}}\\\\times10^\\\\var{PowDiff}\\\\times 10^\\\\var{Pow2-PowDiff}\\\\]</p>\\n<p>\\\\[=\\\\simplify[basic]{{Num1}*10^{Pow1}+{Num2*10^PowDiff}}\\\\times 10^\\\\var{Pow2-PowDiff}.\\\\]</p>\\n<p>Since both numbers have the same power we can now evaluate them as usual to get</p>\\n<p>\\\\[\\\\var{AddNums}\\\\times 10^\\\\var{Pow1}.\\\\]</p>\"", "description": "", "templateType": "long string", "can_override": false}, "AdviceNum2Bigger": {"name": "AdviceNum2Bigger", "group": "Advice", "definition": "\"<p>To add or subtract numbers in standard form we need both of the powers to be the same. We will write both numbers to the power of $\\\\var{Pow2}$. This gives us<br />\\\\[\\\\simplify[basic]{{Num1}*10^{Pow1}+{Num2}}\\\\times 10^\\\\var{Pow2}\\\\]</p>\\n<p>\\\\[=\\\\var{Num1}\\\\times10^\\\\var{-PowDiff}\\\\times \\\\simplify[basic]{10^{Pow1+PowDiff}+{Num2}}\\\\times 10^\\\\var{Pow2}\\\\]</p>\\n<p>\\\\[=\\\\var{Num1*10^-PowDiff}\\\\times \\\\simplify[basic]{10^{Pow1+PowDiff}+{Num2}}\\\\times 10^\\\\var{Pow2}.\\\\]</p>\\n<p>Since both numbers have the same power we can now evaluate them as usual to get</p>\\n<p>\\\\[\\\\var{AddNums}\\\\times 10^\\\\var{Pow2}.\\\\]</p>\"", "description": "", "templateType": "long string", "can_override": false}, "AdviceSamePow": {"name": "AdviceSamePow", "group": "Advice", "definition": "\"<p>To add or subtract numbers in standard form we need both of the powers to be the same. 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