// Numbas version: exam_results_page_options
{"name": "Face, Place and Actual Value  (3 digit integers in base random(2..9))", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"parts": [{"prompt": "<p>Please enter the <strong>face value</strong> of the following digits from the base $\\var{b}$ number $\\var{int}$ in the gaps below.</p>\n<p></p>\n<table border=\"1\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\">Digit</td>\n<td style=\"text-align: center;\">$\\var{hundredsF}$</td>\n<td style=\"text-align: center;\">$\\var{tensF}$</td>\n<td style=\"text-align: center;\">$\\var{units}$</td>\n</tr>\n<tr>\n<td>Face Value</td>\n<td>[[0]]</td>\n<td>[[1]]</td>\n<td>[[2]]</td>\n</tr>\n</tbody>\n</table>", "gaps": [{"correctAnswerFraction": false, "allowFractions": false, "mustBeReducedPC": 0, "marks": 1, "minValue": "hundredsF", "notationStyles": ["plain", "en", "si-en"], "maxValue": "hundredsF", "type": "numberentry", "variableReplacements": [], "showFeedbackIcon": true, "mustBeReduced": false, "scripts": {}, "correctAnswerStyle": "plain", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst"}, {"correctAnswerFraction": false, "allowFractions": false, "mustBeReducedPC": 0, "marks": 1, "minValue": "tensF", "notationStyles": ["plain", "en", "si-en"], "maxValue": "tensF", "type": "numberentry", "variableReplacements": [], "showFeedbackIcon": true, "mustBeReduced": false, "scripts": {}, "correctAnswerStyle": "plain", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst"}, {"correctAnswerFraction": false, "allowFractions": false, "mustBeReducedPC": 0, "marks": 1, "minValue": "units", "notationStyles": ["plain", "en", "si-en"], "maxValue": "units", "type": "numberentry", "variableReplacements": [], "showFeedbackIcon": true, "mustBeReduced": false, "scripts": {}, "correctAnswerStyle": "plain", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst"}], "showFeedbackIcon": true, "marks": 0, "type": "gapfill", "showCorrectAnswer": true, "variableReplacements": [], "scripts": {}, "variableReplacementStrategy": "originalfirst"}, {"prompt": "<p>Please enter the <strong>place value</strong> of the following digits from the base $\\var{b}$ number $\\var{int}$ in the gaps below.</p>\n<p></p>\n<table border=\"1\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\">Digit</td>\n<td style=\"text-align: center;\">$\\var{hundredsF}$</td>\n<td style=\"text-align: center;\">$\\var{tensF}$</td>\n<td style=\"text-align: center;\">$\\var{units}$</td>\n</tr>\n<tr>\n<td>Place Value</td>\n<td>[[0]]</td>\n<td>[[1]]</td>\n<td>[[2]]</td>\n</tr>\n</tbody>\n</table>", "gaps": [{"correctAnswerFraction": false, "allowFractions": false, "mustBeReducedPC": 0, "marks": 1, "minValue": "b^2", "notationStyles": ["plain", "en", "si-en"], "maxValue": "b^2", "type": "numberentry", "variableReplacements": [], "showFeedbackIcon": true, "mustBeReduced": false, "scripts": {}, "correctAnswerStyle": "plain", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst"}, {"correctAnswerFraction": false, "allowFractions": false, "mustBeReducedPC": 0, "marks": 1, "minValue": "b", "notationStyles": ["plain", "en", "si-en"], "maxValue": "b", "type": "numberentry", "variableReplacements": [], "showFeedbackIcon": true, "mustBeReduced": false, "scripts": {}, "correctAnswerStyle": "plain", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst"}, {"correctAnswerFraction": false, "allowFractions": false, "mustBeReducedPC": 0, "marks": 1, "minValue": "1", "notationStyles": ["plain", "en", "si-en"], "maxValue": "1", "type": "numberentry", "variableReplacements": [], "showFeedbackIcon": true, "mustBeReduced": false, "scripts": {}, "correctAnswerStyle": "plain", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst"}], "showFeedbackIcon": true, "marks": 0, "type": "gapfill", "showCorrectAnswer": true, "variableReplacements": [], "scripts": {}, "variableReplacementStrategy": "originalfirst"}, {"prompt": "<p>Please enter the <strong>actual value</strong> of the following digits from the base $\\var{b}$ number $\\var{int}$ in the gaps below.</p>\n<p></p>\n<table border=\"1\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\">Digit</td>\n<td style=\"text-align: center;\">$\\var{hundredsF}$</td>\n<td style=\"text-align: center;\">$\\var{tensF}$</td>\n<td style=\"text-align: center;\">$\\var{units}$</td>\n</tr>\n<tr>\n<td>Actual Value</td>\n<td>[[0]]</td>\n<td>[[1]]</td>\n<td>[[2]]</td>\n</tr>\n</tbody>\n</table>", "gaps": [{"correctAnswerFraction": false, "allowFractions": false, "mustBeReducedPC": 0, "marks": 1, "minValue": "hundredsA", "notationStyles": ["plain", "en", "si-en"], "maxValue": "hundredsA", "type": "numberentry", "variableReplacements": [], "showFeedbackIcon": true, "mustBeReduced": false, "scripts": {}, "correctAnswerStyle": "plain", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst"}, {"correctAnswerFraction": false, "allowFractions": false, "mustBeReducedPC": 0, "marks": 1, "minValue": "tensA", "notationStyles": ["plain", "en", "si-en"], "maxValue": "tensA", "type": "numberentry", "variableReplacements": [], "showFeedbackIcon": true, "mustBeReduced": false, "scripts": {}, "correctAnswerStyle": "plain", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst"}, {"correctAnswerFraction": false, "allowFractions": false, "mustBeReducedPC": 0, "marks": 1, "minValue": "units", "notationStyles": ["plain", "en", "si-en"], "maxValue": "units", "type": "numberentry", "variableReplacements": [], "showFeedbackIcon": true, "mustBeReduced": false, "scripts": {}, "correctAnswerStyle": "plain", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst"}], "showFeedbackIcon": true, "marks": 0, "type": "gapfill", "showCorrectAnswer": true, "variableReplacements": [], "scripts": {}, "variableReplacementStrategy": "originalfirst"}, {"prompt": "<p>Hence the base $\\var{b}$ number $\\var{int}$ is equal to [[0]]&nbsp;in base 10.</p>", "gaps": [{"correctAnswerFraction": false, "allowFractions": false, "mustBeReducedPC": 0, "marks": 1, "minValue": "valueinbase10", "notationStyles": ["plain", "en", "si-en"], "maxValue": "valueinbase10", "type": "numberentry", "variableReplacements": [], "showFeedbackIcon": true, "mustBeReduced": false, "scripts": {}, "correctAnswerStyle": "plain", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst"}], "showFeedbackIcon": true, "marks": 0, "type": "gapfill", "showCorrectAnswer": true, "variableReplacements": [], "scripts": {}, "variableReplacementStrategy": "originalfirst"}], "preamble": {"css": "", "js": ""}, "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"int": {"name": "int", "description": "", "definition": "latex(join(listOfDigits,'')+'_\\\\var\\{btext\\}')", "group": "Ungrouped variables", "templateType": "anything"}, "units": {"name": "units", "description": "", "definition": "listOfDigits[2]", "group": "Ungrouped variables", "templateType": "anything"}, "tensA": {"name": "tensA", "description": "", "definition": "tensF*b", "group": "Ungrouped variables", "templateType": "anything"}, "tensF": {"name": "tensF", "description": "", "definition": "listOfDigits[1]", "group": "Ungrouped variables", "templateType": "anything"}, "hundredsA": {"name": "hundredsA", "description": "", "definition": "hundredsF*b^2", "group": "Ungrouped variables", "templateType": "anything"}, "btext": {"name": "btext", "description": "", "definition": "switch(b=2,'two', b=3, 'three', b=4, 'four', b=5, 'five', b=6, 'six', b=7,'seven', b=8, 'eight','nine')", "group": "Ungrouped variables", "templateType": "anything"}, "valueinbase10": {"name": "valueinbase10", "description": "", "definition": "hundredsA+tensA+units", "group": "Ungrouped variables", "templateType": "anything"}, "b": {"name": "b", "description": "", "definition": "random(2..9)", "group": "Ungrouped variables", "templateType": "anything"}, "otherDigits": {"name": "otherDigits", "description": "<p>don't want repeated digits unless we really need to (binary)</p>", "definition": "if(b=2,shuffle(0..b-1)[0..2],shuffle(0..b-1 except hundredsF)[0..2])", "group": "try this", "templateType": "anything"}, "listOfDigits": {"name": "listOfDigits", "description": "", "definition": "[hundredsF]+otherDigits", "group": "try this", "templateType": "anything"}, "hundredsF": {"name": "hundredsF", "description": "", "definition": "random(1..b-1)", "group": "try this", "templateType": "anything"}}, "advice": "<p>a) The&nbsp;<strong>face value</strong> of a digit is simply the digit itself. It is all about what the digit looks like.</p>\n<p>For example, the face value of $2$ in the base $5$ number $1234_{\\text{five}}$ is just $2$.</p>\n<p>b) The&nbsp;<strong>place value</strong> of a digit is the 'value' of the 'column' it is written in. It is all about where the digit is. Place values are always powers of the base.</p>\n<p>Place values are always powers of the base. Recall in base $10$ we have a <g class=\"gr_ gr_30 gr-alert gr_gramm gr_inline_cards gr_run_anim Grammar multiReplace\" id=\"30\" data-gr-id=\"30\">thousands</g> column, a hundreds column, a tens column and a units/<g class=\"gr_ gr_29 gr-alert gr_gramm gr_inline_cards gr_run_anim Grammar multiReplace\" id=\"29\" data-gr-id=\"29\">ones</g> column. The place value for something in the thousands column is $1000=10^3$, the place value for something in the hundreds column is $100=10^2$, the place value for something in the tens column is $10=10^1$ and the place value for something in the units/<g class=\"gr_ gr_31 gr-alert gr_gramm gr_inline_cards gr_run_anim Grammar multiReplace\" id=\"31\" data-gr-id=\"31\">ones</g> column is $1=10^0$. However, in base $5$, for example, &nbsp;</p>\n<ul>\n<li>the $4$ in&nbsp;$1234_{\\text{five}}$ has a place value of $5^0=1$ and so is in units/ones column</li>\n<li>the $3$ in&nbsp;$1234_{\\text{five}}$ has a place value of $5^1=5$ and so is in 'fives' column</li>\n<li>the $2$ in&nbsp;$1234_{\\text{five}}$ has a place value of $5^2=25$ and so is in 'twenty-fives' column</li>\n<li>the $1$ in&nbsp;$1234_{\\text{five}}$ has a place value of $5^3=125$ and so is in 'hundred and twenty-fives' column</li>\n</ul>\n<p>c) The&nbsp;<strong>actual value</strong> of a digit is the face value times the place value. It is all about what that digit actually adds/brings to the number, what it is actually worth or what it actually represents.</p>\n<p>For example, the actual value of the digit $2$ in the number $1234_{\\text{five}}$ is $2\\times 5^2=50$ (the $2$ in $1234_{\\text{five}}$ actually stands for $50$).</p>", "extensions": [], "functions": {}, "metadata": {"description": "<p>Integers in&nbsp;bases from 2 to 9 and converting them to base 10.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "variable_groups": [{"name": "try this", "variables": ["hundredsF", "otherDigits", "listOfDigits"]}], "tags": [], "ungrouped_variables": ["b", "int", "hundredsA", "tensF", "tensA", "units", "valueinbase10", "btext"], "name": "Face, Place and Actual Value  (3 digit integers in base random(2..9))", "rulesets": {}, "statement": "<p>In our usual number <g class=\"gr_ gr_7 gr-alert gr_gramm gr_inline_cards gr_run_anim Punctuation only-ins replaceWithoutSep\" id=\"7\" data-gr-id=\"7\">system</g> we only have ten digits ($0$ to $9$). We call this the base $10$ system. The place value of numbers <g class=\"gr_ gr_8 gr-alert gr_gramm gr_inline_cards gr_run_anim Grammar multiReplace\" id=\"8\" data-gr-id=\"8\">are</g> based on the powers of 10.</p>\n<p>In the base $\\var{b}$ system we only have $\\var{b}$ digits ($0$ to $\\var{b-1}$) and the place values are based on powers of $\\var{b}$.</p>", "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/"}]}