// Numbas version: exam_results_page_options {"name": "Powers of ten practice", "metadata": {"description": "", "licence": "None specified"}, "duration": 0, "percentPass": 0, "showQuestionGroupNames": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", "", ""], "questions": [{"name": "Powers of ten practice_easy_1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Nick Walker", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2416/"}], "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International"}, "preamble": {"css": "", "js": ""}, "tags": [], "advice": "

The best way to approach this sort of calculation is to follow the following rules;

1) Remember that 10^x $\\times$ 10^y = 10^(x+y)

2) Remember that 10^x $\\div$ 10^y =10^(x-y)

so you can answer this question by collecting the exponents, then following the above rules, which will give you the exponent for your final answer;

\\[(\\var{randomiser1})-(\\var{randomiser2})=\\var{log_result}\\]

....which leads to a final answer of;

\\[=10^{\\var{log_result}}\\]

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The result of;

$\\frac{10^{\\var{randomiser1}}}{10^{\\var{randomiser2}}}$

is;

10^[[0]]

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The result of;

$\\frac{10^{\\var{randomiser1}}\\times10^{\\var{randomiser3}}}{10^{\\var{randomiser2}}\\times10^{\\var{randomiser4}}}$

is;

10^[[0]]

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The best way to approach this sort of calculation is to follow the following rules;

1) Remember that 10^x $\\times$ 10^y = 10^(x+y)

2) Remember that 10^x $\\div$ 10^y =10^(x-y)

so you can answer this question by collecting the exponents, then following the above rules, which will give you the exponent for your final answer;

\\[(\\var{randomiser1}+\\var{randomiser3})-(\\var{randomiser2}+\\var{randomiser4})=\\var{log_result}\\]

....which leads to a final answer of;

\\[=10^{\\var{log_result}}\\]

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The result of;

$\\frac{(10^{\\var{randomiser1}}\\times10^{\\var{randomiser3}})^\\var{randomiser5}}{10^{\\var{randomiser2}}\\times10^{\\var{randomiser4}}}$

is;

10^[[0]]

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The best way to approach this sort of calculation is to follow the following rules;

1) 10^x $\\times$ 10^y = 10^(x+y)

2) 10^x $\\div$ 10^y =10^(x-y)

3) (10^x)^y = 10^{(x$\\times$y)}

so you can answer this question by collecting the exponents, then following the above rules, which will give you the exponent for your final answer;

\\[((\\var{randomiser1}+\\var{randomiser3})\\times \\var{randomiser5})-(\\var{randomiser2}+\\var{randomiser4})=\\var{log_result}\\]

....which leads to a final answer of;

\\[=10^{\\var{log_result}}\\]

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A good way to start is to reorganise the calculation as follows;

\\[\\frac{\\var{coeff1}\\times\\var{coeff2}}{\\var{coeff3}\\times\\var{coeff4}}\\times\\frac{10^{\\var{randomiser1}}\\times10^{\\var{randomiser2}}}{10^{\\var{randomiser3}}\\times{10^{\\var{randomiser4}}}} \\]

Then you can calculate the result of the first term above;

\\[\\frac{\\var{coeff1}\\times\\var{coeff2}}{\\var{coeff3}\\times\\var{coeff4}} = \\var{coeff_result_crude}\\]

and follow these rules to determine the power of ten required in the second term;

1) Remember that 10^x $\\times$ 10^y = 10^(x+y)

2) Remember that 10^x $\\div$ 10^y =10^(x-y)

collecting the exponents and following the above rules will give you the exponent of ten required in your final answer;

\\[(\\var{randomiser1}+\\var{randomiser2})-(\\var{randomiser3}+\\var{randomiser4})=\\var{log_result_crude}\\]

....which leads to a final answer of;

\\[\\var{coeff_result_crude}\\times10^{\\var{log_result_crude}}\\]

You should display your final answer in \"standard form\", which means that you have one digit before the decimal place as follows;

\\[\\var{coeff_result}\\times10^{\\var{log_result}}\\]

but in an examination, it would not be necessary for an answer to be in standard form to be marked correct (provided the value is correct).

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"Unnamed group", "variables": []}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "student_significand (The significand as the student entered it):\n parsenumber(studentanswer[0],\"en\")\n\nsignificand_size (If student's significand is written a*10^n, 1<=a<10, this is n):\n floor(log(abs(student_significand)))\n\nstudent_exponent (The exponent as the student wrote it):\n parsenumber(studentanswer[1],\"en\")\n\nnumbers_ok:\n assert(not isnan(student_significand),\n fail(\"Your significand is not a valid number.\")\n );\n assert(not isnan(student_exponent),\n fail(\"Your exponent is not a valid number.\")\n )\n\nadjusted_exponent (The exponent of the student's number, taking into account the size of their significand): \n student_exponent + significand_size\n\nadjusted_significand (The student's significand, scaled into the range 1..10):\n student_significand/(10^significand_size)\n\nsignificand_correct (Is the adjusted significand correct?):\n feedback(\"\");\n let(result,mark_part(gaps[0][\"path\"],string(adjusted_significand)),\n result[\"credit\"]=1\n )\n\nexponent_correct (Is the adjusted exponent correct?):\n feedback(\"Feedback:\");\n let(result,mark_part(gaps[1][\"path\"],string(adjusted_exponent)),\n result[\"credit\"]=1\n )\n\ncorrect:\n correctif(significand_correct and exponent_correct)\n\nmark:\n apply(significand_correct);\n apply(exponent_correct);\n apply(numbers_ok);\n apply(correct)\n\nsubmit_gaps:\n map(\n try(\n submit_part(gaps[gap_number][\"path\"],answer),\n err,\n fail(translate(\"part.gapfill.error marking gap\",[\"name\": gaps[gap_number][\"name\"], \"message\": err]))\n ),\n [gap_number,answer],\n zip(0..1,studentAnswer)\n )\n\ninterpreted_answer: [adjusted_significand, adjusted_exponent]", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

The result of;

$\\frac{\\var{coeff1} \\times 10^{\\var{randomiser1}}\\times\\var{coeff2} \\times 10^{\\var{randomiser2}}}{\\var{coeff3} \\times 10^{\\var{randomiser3}}\\times\\var{coeff4} \\times 10^{\\var{randomiser4}}}$

is;

[[0]]$\\times$10^[[1]]

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