// Numbas version: exam_results_page_options {"name": "Units: converting between different prefixes 1D (nano to giga)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"advice": "

Write the following questions down on paper and evaluate them without using a calculator.

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If you are unsure of how to do a question, click on Show steps to see the full working. Then, once you understand how to do the question, click on Try another question like this one to start again.

", "parts": [{"prompt": "

$\\var{mult[0]}\\, \\var{P0[0]}\\var{units[0][0]} =$ [[0]] $\\var{P1[0]}\\var{units[0][0]}$

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", "scripts": {}, "gaps": [{"precisionType": "sigfig", "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "customMarkingAlgorithm": "", "correctAnswerStyle": "plain", "unitTests": [], "maxValue": "{ansa}", "strictPrecision": false, "precisionPartialCredit": 0, "type": "numberentry", "mustBeReducedPC": 0, "minValue": "{ansa}", "extendBaseMarkingAlgorithm": true, "allowFractions": false, "variableReplacements": [], "showPrecisionHint": false, "precisionMessage": "You have not given your answer to the correct precision.", "correctAnswerFraction": false, "mustBeReduced": false, "precision": "4", "showCorrectAnswer": true, "marks": 1, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst"}], "steps": [{"prompt": "

The following are some of the common SI prefixes used list in decending order. The scaling factor between each adjacent prefix is $10^3=1000$.

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giga
mega
kilo
base unit
milli
micro
nano

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The scaling factor between {P0[2]} and {P1[2]} is therefore

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(10^3)^\\var{thousandsa}=10^\\var{apowerdiff}=\\simplify{10^{apowerdiff}}. \n \n When converting from {P0[2]+units[0][1]} to {P1[2]+units[0][1]} the units are getting larger and so the the number will have to get smaller. That is, we will divide by \\simplify{10^{apowerdiff}} to convert from {P0[2]+units[0][1]} to {P1[2]+units[0][1]}. Recall dividing by \\simplify{10^{apowerdiff}} is simply moving the decimal place to the left \\var{apowerdiff} places in order to make the number smaller. \n \n Therefore, \\begin{align}\\var{mult[0]} \\,\\var{P0[0]}\\var{units[0][0]}&=\\left(\\var{mult[0]} \\div\\simplify{10^{P1[3]-P0[3]}} \\right)\\,\\var{P1[0]}\\var{units[0][0]}\\\\&=\\var{ansa}\\,\\var{P1[0]}\\var{units[0][0]}.\\end{align} \n \n If this doesn't make sense to you consider a simpler example. 5 one-dollar coins is the same amount of money as 1 five-dollar note. As the units get bigger you need less of them to have the same amount of money. In this example the scaling factor would be 5 since the size of the units increases by a factor of 5 and the number of units decreases by a factor of 5. Now, say we had 20 one-dollar coins and we wanted to convert this to five-dollar notes, we would calculate 20\\div 5 which equals 4 and therefore we would get 4 five-dollar notes. \n \n ", "scripts": {}, "type": "information", "showCorrectAnswer": true, "variableReplacements": [], "unitTests": [], "marks": 0, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst"}], "sortAnswers": false, "customMarkingAlgorithm": "", "marks": 0, "type": "gapfill", "showCorrectAnswer": true, "stepsPenalty": "1", "unitTests": [], "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "variableReplacements": []}, {"prompt": " \\var{mult[1]}\\, \\var{P2[0]}\\var{units[1][0]} = [[0]] \\var{P3[0]}\\var{units[1][0]} ", "scripts": {}, "gaps": [{"precisionType": "sigfig", "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "customMarkingAlgorithm": "", "correctAnswerStyle": "plain", "unitTests": [], "maxValue": "{ansb}", "strictPrecision": false, "precisionPartialCredit": 0, "type": "numberentry", "mustBeReducedPC": 0, "minValue": "{ansb}", "extendBaseMarkingAlgorithm": true, "allowFractions": false, "variableReplacements": [], "showPrecisionHint": false, "precisionMessage": "You have not given your answer to the correct precision.", "correctAnswerFraction": false, "mustBeReduced": false, "precision": "4", "showCorrectAnswer": true, "marks": 1, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst"}], "steps": [{"prompt": " The following are some of the common SI prefixes used list in decending order. The scaling factor between each adjacent prefix is 10^3=1000. \n giga mega kilo base unit milli micro nano \n \n The scaling factor between {P2[2]} and {P3[2]} is therefore \n (10^3)^\\var{thousandsb}=10^\\var{bpowerdiff}=\\simplify{10^{bpowerdiff}}.

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When converting from {P2[2]+units[1][1]} to {P3[2]+units[1][1]} the units are getting smaller and so the the number will have to get bigger. That is, we will multiply by $\\simplify{10^{bpowerdiff}}$ to convert from {P2[2]+units[1][1]} to {P3[2]+units[1][1]}. Recall multiplying by $\\simplify{10^{bpowerdiff}}$ is simply moving the decimal place to the right $\\var{bpowerdiff}$ places in order to make the number larger.

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Therefore, \\begin{align}\\var{mult[1]} \\,\\var{P2[0]}\\var{units[1][0]}&=\\left(\\var{mult[1]} \\times\\simplify{10^{bpowerdiff}} \\right)\\,\\var{P3[0]}\\var{units[1][0]}\\\\&=\\var{ansb}\\,\\var{P3[0]}\\var{units[1][0]}.\\end{align}

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If this doesn't make sense to you consider a simpler example. $1$ five-dollar note is the same amount of money as $5$ one-dollar coins. As the units get smaller you need more of them to have the same amount of money. In this example the scaling factor would be $5$ since the size of the units decreases by a factor of $5$ and the number of units increases by a factor of $5$. Now, say we had $4$ five-dollar notes and we wanted to convert this to one-dollar coins, we would calculate $4\\times 5$ which equals $20$ and therefore we would get $20$ one-dollar coins.

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random pair 1 - designed to be increasing

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random pair 2 - designed to be decreasing

", "group": "Ungrouped variables", "templateType": "anything", "definition": "if(random_order[2]>random_order[3],random_order[2..4],[random_order[3],random_order[2]])", "name": "RP2"}, "bpowerdiff": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "P2[3]-P3[3]", "name": "bpowerdiff"}, "P0": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "prefix[RP1[0]]", "name": "P0"}, "thousandsb": {"description": "", "group": "Ungrouped variables", "templateType": "anything", "definition": "(P2[3]-P3[3])/3", "name": "thousandsb"}}, "preamble": {"js": "", "css": ""}, "variable_groups": [], "ungrouped_variables": ["prefix", "units", "mult", "random_order", "RP1", "RP2", "P0", "P1", "P2", "P3", "ansa", "apowerdiff", "ansb", "bpowerdiff", "thousandsa", "thousandsb"], "metadata": {"description": "

Converting between giga, mega, kilo, base, milli and micro, nano. Metres, grams and litres.

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "functions": {}, "statement": "

Write the following questions down on paper and evaluate them without using a calculator.

\n

If you are unsure of how to do a question, click on Show steps to see the full working. Then, once you understand how to do the question, click on Try another question like this one to start again.

", "tags": [], "name": "Units: converting between different prefixes 1D (nano to giga)", "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/"}]}