// Numbas version: exam_results_page_options {"name": "Intro to our number system/decimals", "metadata": {"description": "", "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": "Large numbers: how to read (short scale)", "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": "Daniel Sutherland", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/16947/"}], "tags": [], "metadata": {"description": "

Primarily concerned with identifying when a number is in the thousands, million, billions or trillions.

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

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.

The number $\\var{large_display[0]}$ is equal to \"[[0]] {offset[0][1]}\".

", "stepsPenalty": "1", "steps": [{"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": "

The following table gives the place value or name of many of the 'columns'.

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n

Numeral		Place value of $1$
$1\\,000$		One Thousand
$10\\,000$		Ten Thousand
$100\\,000$		One Hundred Thousand
$1\\,000\\,000$		One Million
$10\\,000\\,000$		Ten Million
$100\\,000\\,000$		One Hundred Million
$1\\,000\\,000\\,000$		One Billion
$10\\,000\\,000\\,000$		Ten Billion
$100\\,000\\,000\\,000$		One Hundred Billion
$1\\,000\\,000\\,000\\,000$		One Trillion
$\\vdots$		$\\vdots$

In particular, $\\var{large_display[0]}$ is equal to $\\var{sig_figs[0]}$ lots of one {offset[0][1]}, and is read as $\\var{sig_figs[0]}$ {offset[0][1]}.

The number $\\var{large_display[1]}$ is equal to \"[[0]] {offset[1][1]}\".

The following table gives the place value or name of many of the 'columns'.

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n

Numeral		Place value of $1$
$1\\,000$		One Thousand
$10\\,000$		Ten Thousand
$100\\,000$		One Hundred Thousand
$1\\,000\\,000$		One Million
$10\\,000\\,000$		Ten Million
$100\\,000\\,000$		One Hundred Million
$1\\,000\\,000\\,000$		One Billion
$10\\,000\\,000\\,000$		Ten Billion
$100\\,000\\,000\\,000$		One Hundred Billion
$1\\,000\\,000\\,000\\,000$		One Trillion
$\\vdots$		$\\vdots$

In particular, $\\var{large_display[1]}$ is equal to $\\var{sig_figs[1]}$ lots of one {offset[1][1]}, and is read as $\\var{sig_figs[1]}$ {offset[1][1]}.

The number $\\var{large_display[2]}$ is equal to \"[[0]] {offset[2][1]}\".

The following table gives the place value or name of many of the 'columns'.

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n

Numeral		Place value of $1$
$1\\,000$		One Thousand
$10\\,000$		Ten Thousand
$100\\,000$		One Hundred Thousand
$1\\,000\\,000$		One Million
$10\\,000\\,000$		Ten Million
$100\\,000\\,000$		One Hundred Million
$1\\,000\\,000\\,000$		One Billion
$10\\,000\\,000\\,000$		Ten Billion
$100\\,000\\,000\\,000$		One Hundred Billion
$1\\,000\\,000\\,000\\,000$		One Trillion
$\\vdots$		$\\vdots$

In particular, $\\var{large_display[2]}$ is equal to $\\var{sig_figs[2]}$ lots of one {offset[2][1]}, and is read as $\\var{sig_figs[2]}$ {offset[2][1]}.

Primarily concerned with identifying when a number is in the thousands, million, billions or trillions.

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

", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"offset": {"name": "offset", "group": "Ungrouped variables", "definition": "[random(\n [1000000, 'million'],\n [1000000000, 'billion'],\n [1000000000000, 'trillion']\n)]+[random(\n [1000000000, 'billion'],\n [1000000000000, 'trillion']\n),[1000000000000, 'trillion']]", "description": "", "templateType": "anything", "can_override": false}, "large": {"name": "large", "group": "Ungrouped variables", "definition": "[sig_figs[0]*offset[0][0], sig_figs[1]*offset[1][0],sig_figs[2]*offset[2][0]]", "description": "", "templateType": "anything", "can_override": false}, "sig_figs": {"name": "sig_figs", "group": "Ungrouped variables", "definition": "shuffle([random(2..9), random(10..90#10),random(101..999)])", "description": "", "templateType": "anything", "can_override": false}, "large_display": {"name": "large_display", "group": "Ungrouped variables", "definition": "[latex(join(split(dpformat(large[0],0,'si-en'),\" \"),\"\\\\ \")), latex(join(split(dpformat(large[1],0,'si-en'),\" \"),\"\\\\ \")),\nlatex(join(split(dpformat(large[0]/10,0,'si-en'),\" \"),\"\\\\ \")),latex(join(split(dpformat(large[0]/100,0,'si-en'),\" \"),\"\\\\ \")),latex(join(split(dpformat(large[0]/1000,0,'si-en'),\" \"),\"\\\\ \")),\nlatex(join(split(dpformat(large[1]/10,0,'si-en'),\" \"),\"\\\\ \")),latex(join(split(dpformat(large[1]/100,0,'si-en'),\" \"),\"\\\\ \")),latex(join(split(dpformat(large[1]/1000,0,'si-en'),\" \"),\"\\\\ \")),\nlatex(join(split(dpformat(large[1]/10000,0,'si-en'),\" \"),\"\\\\ \")),latex(join(split(dpformat(large[1]/100000,0,'si-en'),\" \"),\"\\\\ \")),latex(join(split(dpformat(large[1]/1000000,0,'si-en'),\" \"),\"\\\\ \")),\nlatex(join(split(dpformat(large[2],0,'si-en'),\" \"),\"\\\\ \")),\nlatex(join(split(dpformat(large[2]/1000,0,'si-en'),\" \"),\"\\\\ \")),latex(join(split(dpformat(large[2]/1000000,0,'si-en'),\" \"),\"\\\\ \")),latex(join(split(dpformat(large[2]/1000000000,0,'si-en'),\" \"),\"\\\\ \")),]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["offset", "sig_figs", "large", "large_display"], "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": "

The number $\\var{large_display[0]}$ is equal to [[0]] thousands.

The following table gives the place value or name of many of the 'columns'.

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n

Numeral		Place value of $1$
$1\\,000$		One Thousand
$10\\,000$		Ten Thousand
$100\\,000$		One Hundred Thousand
$1\\,000\\,000$		One Million
$10\\,000\\,000$		Ten Million
$100\\,000\\,000$		One Hundred Million
$1\\,000\\,000\\,000$		One Billion
$10\\,000\\,000\\,000$		Ten Billion
$100\\,000\\,000\\,000$		One Hundred Billion
$1\\,000\\,000\\,000\\,000$		One Trillion
$\\vdots$		$\\vdots$

The place value of each column is based on the number ten, each adjacent column is either ten times larger or smaller (depending on which direction you are heading).

So even though $\\var{large_display[0]}$ is correctly read as $\\var{sig_figs[0]}$ {offset[0][1]},

it is also equal to

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n

$\\var{large_display[0]}$		ones
{large_display[2]}		tens
{large_display[3]}		hundreds
{large_display[4]}		thousands
$\\vdots$		$\\vdots$

The number $\\var{large_display[1]}$ is equal to [[0]] millions.

The following table gives the place value or name of many of the 'columns'.

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n

Numeral		Place value of $1$
$1\\,000$		One Thousand
$10\\,000$		Ten Thousand
$100\\,000$		One Hundred Thousand
$1\\,000\\,000$		One Million
$10\\,000\\,000$		Ten Million
$100\\,000\\,000$		One Hundred Million
$1\\,000\\,000\\,000$		One Billion
$10\\,000\\,000\\,000$		Ten Billion
$100\\,000\\,000\\,000$		One Hundred Billion
$1\\,000\\,000\\,000\\,000$		One Trillion
$\\vdots$		$\\vdots$

The place value of each column is based on the number ten, each adjacent column is either ten times larger or smaller (depending on which direction you are heading).

So even though $\\var{large_display[1]}$ is correctly read as $\\var{sig_figs[1]}$ {offset[1][1]},

it is also equal to

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n

$\\var{large_display[1]}$		ones
{large_display[5]}		tens
{large_display[6]}		hundreds
{large_display[7]}		thousands
{large_display[8]}		ten thousands
{large_display[9]}		hundred thousands
{large_display[10]}		millions
$\\vdots$		$\\vdots$

The number $\\var{large_display[11]}$ is equal to [[0]] billions.

The following table gives the place value or name of many of the 'columns'.

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n

Numeral		Place value of $1$
$1\\,000$		One Thousand
$10\\,000$		Ten Thousand
$100\\,000$		One Hundred Thousand
$1\\,000\\,000$		One Million
$10\\,000\\,000$		Ten Million
$100\\,000\\,000$		One Hundred Million
$1\\,000\\,000\\,000$		One Billion
$10\\,000\\,000\\,000$		Ten Billion
$100\\,000\\,000\\,000$		One Hundred Billion
$1\\,000\\,000\\,000\\,000$		One Trillion
$\\vdots$		$\\vdots$

The place value of each column is based on the number ten, each adjacent column is either ten times larger or smaller (depending on which direction you are heading).

So even though $\\var{large_display[11]}$ is correctly read as $\\var{sig_figs[2]}$ {offset[2][1]},

it is also equal to

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n

$\\var{large_display[11]}$		ones
{large_display[12]}		thousands
{large_display[13]}		millions
{large_display[14]}		billions
$\\vdots$		$\\vdots$

"}], "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "large[2]/1000000000", "maxValue": "large[2]/1000000000", "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": "Decimals: how to read", "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/"}], "tags": [], "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"place": {"name": "place", "group": "Ungrouped variables", "definition": "random([placedig*0.001, \"tenths\", \"hundredths\", \"thousandths\" ]\n,[placedig*0.01, \"tenths\", \"thousandths\", \"hundredths\"],\n [placedig*0.1, \"thousandths\", \"hundredths\", \"tenths\"])", "description": "", "templateType": "anything", "can_override": false}, "pron": {"name": "pron", "group": "Ungrouped variables", "definition": "shuffle([random(\n[dpformat(0.10, 2), \"one zero\", \"ten\"], \n[dpformat(0.11, 2), \"one one\", \"eleven\"], \n[dpformat(0.12, 2), \"one two\", \"twelve\"],\n[dpformat(0.13, 2), \"one three\", \"thirteen\"],\n[dpformat(0.14, 2), \"one four\", \"fourteen\"],\n[dpformat(0.15, 2), \"one five\", \"fifteen\"],\n[dpformat(0.16, 2), \"one six\", \"sixteen\"],\n[dpformat(0.17, 2), \"one seven\", \"seventeen\"],\n[dpformat(0.18, 2), \"one eight\", \"eighteen\"],\n[dpformat(0.19, 2), \"one nine\", \"ninteen\"], \n\n[dpformat(0.20, 2), \"two zero\", \"twenty\"], \n[dpformat(0.21, 2), \"two one\", \"twenty one\"], \n[dpformat(0.22, 2), \"two two\", \"twenty two\"],\n[dpformat(0.23, 2), \"two three\", \"twenty three\"],\n[dpformat(0.24, 2), \"two four\", \"twenty four\"], \n[dpformat(0.25, 2), \"two five\", \"twenty five\"],\n[dpformat(0.26, 2), \"two six\", \"twenty six\"],\n[dpformat(0.27, 2), \"two seven\", \"twenty seven\"],\n[dpformat(0.28, 2), \"two eight\", \"twenty eight\"],\n[dpformat(0.29, 2), \"two nine\", \"twenty nine\"], \n \n[dpformat(0.30, 2), \"three zero\", \"thirty\"], \n[dpformat(0.31, 2), \"three one\", \"thirty one\"], \n[dpformat(0.32, 2), \"three two\", \"thirty two\"],\n[dpformat(0.33, 2), \"three three\", \"thirty three\"],\n[dpformat(0.34, 2), \"three four\", \"thirty four\"], \n[dpformat(0.35, 2), \"three five\", \"thirty five\"],\n[dpformat(0.36, 2), \"three six\", \"thirty six\"],\n[dpformat(0.37, 2), \"three seven\", \"thirty seven\"],\n[dpformat(0.38, 2), \"three eight\", \"thirty eight\"],\n[dpformat(0.39, 2), \"three nine\", \"thirty nine\"], \n \n[dpformat(0.40, 2), \"four zero\", \"forty\"], \n[dpformat(0.41, 2), \"four one\", \"forty one\"], \n[dpformat(0.42, 2), \"four two\", \"forty two\"],\n[dpformat(0.43, 2), \"four three\", \"forty three\"],\n[dpformat(0.44, 2), \"four four\", \"forty four\"], \n[dpformat(0.45, 2), \"four five\", \"forty five\"],\n[dpformat(0.46, 2), \"four six\", \"forty six\"],\n[dpformat(0.47, 2), \"four seven\", \"forty seven\"],\n[dpformat(0.48, 2), \"four eight\", \"forty eight\"],\n[dpformat(0.49, 2), \"four nine\", \"forty nine\"], \n \n[dpformat(0.50, 2), \"five zero\", \"fifty\"], \n[dpformat(0.51, 2), \"five one\", \"fifty one\"], \n[dpformat(0.52, 2), \"five two\", \"fifty two\"],\n[dpformat(0.53, 2), \"five three\", \"fifty three\"],\n[dpformat(0.54, 2), \"five four\", \"fifty four\"], \n[dpformat(0.55, 2), \"five five\", \"fifty five\"],\n[dpformat(0.56, 2), \"five six\", \"fifty six\"],\n[dpformat(0.57, 2), \"five seven\", \"fifty seven\"],\n[dpformat(0.58, 2), \"five eight\", \"fifty eight\"],\n[dpformat(0.59, 2), \"five nine\", \"fifty nine\"], \n \n[dpformat(0.60, 2), \"six zero\", \"sixty\"], \n[dpformat(0.70, 2), \"seven zero\", \"seventy\"], \n[dpformat(0.80, 2), \"eight zero\", \"eighty\"], \n[dpformat(0.90, 2), \"nine zero\", \"ninety\"], \n)]+[random(\n[dpformat(0.100, 3), \"one zero zero\", \"one hundred\"], \n[dpformat(0.200, 3), \"two zero zero\", \"two hundred\"], \n[dpformat(0.300, 3), \"three zero zero\", \"three hundred\"],\n[dpformat(0.400, 3), \"four zero zero\", \"four hundred\"],\n[dpformat(0.500, 3), \"five zero zero\", \"five hundred\"], \n[dpformat(0.600, 3), \"six zero zero\", \"six hundred\"],\n[dpformat(0.700, 3), \"seven zero zero\", \"seven hundred\"],\n[dpformat(0.800, 3), \"eight zero zero\", \"eight hundred\"],\n[dpformat(0.900, 3), \"nine zero zero\", \"nine hundred\"],\n[dpformat(0.120, 3), \"one two zero\", \"one hundred and twenty\"], \n[dpformat(0.230, 3), \"two three zero\", \"two hundred and thirty\"], \n[dpformat(0.340, 3), \"three four zero\", \"three hundred and forty\"],\n[dpformat(0.450, 3), \"four five zero\", \"four hundred and fifty\"],\n[dpformat(0.501, 3), \"five zero one\", \"five hundred and one\"], \n[dpformat(0.602, 3), \"six zero two\", \"six hundred and two\"],\n[dpformat(0.703, 3), \"seven zero three\", \"seven hundred and three\"],\n[dpformat(0.804, 3), \"eight zero four\", \"eight hundred and four\"],\n[dpformat(0.905, 3), \"nine zero five\", \"nine hundred and five\"]\n )])\n ", "description": "", "templateType": "anything", "can_override": false}, "placedig": {"name": "placedig", "group": "Ungrouped variables", "definition": "random(1..9)", "description": "", "templateType": "anything", "can_override": false}, "hundredths": {"name": "hundredths", "group": "Ungrouped variables", "definition": "if(len(pron[0][0])=4,dec(pron[0][0])*100,dec(pron[1][0])*100)", "description": "", "templateType": "anything", "can_override": false}, "pron2": {"name": "pron2", "group": "Ungrouped variables", "definition": "random(\n[dpformat(0.100, 3), \"zero point one zero zero\", \"zero point one hundred\"], \n[dpformat(0.200, 3), \"zero point two zero zero\", \"zero point two hundred\"], \n[dpformat(0.300, 3), \"zero point three zero zero\", \"zero point three hundred\"],\n[dpformat(0.400, 3), \"zero point four zero zero\", \"zero point four hundred\"],\n[dpformat(0.500, 3), \"zero point five zero zero\", \"zero point five hundred\"], \n[dpformat(0.600, 3), \"zero point six zero zero\", \"zero point six hundred\"],\n[dpformat(0.700, 3), \"zero point seven zero zero\", \"zero point seven hundred\"],\n[dpformat(0.800, 3), \"zero point eight zero zero\", \"zero point eight hundred\"],\n[dpformat(0.900, 3), \"zero point nine zero zero\", \"zero point nine hundred\"],\n[dpformat(0.120, 3), \"zero point one two zero\", \"zero point one hundred and twenty\"], \n[dpformat(0.230, 3), \"zero point two three zero\", \"zero point two hundred and thirty\"], \n[dpformat(0.340, 3), \"zero point three four zero\", \"zero point three hundred and forty\"],\n[dpformat(0.450, 3), \"zero point four five zero\", \"zero point four hundred and fifty\"],\n[dpformat(0.501, 3), \"zero point five zero one\", \"zero point five hundred and one\"], \n[dpformat(0.602, 3), \"zero point six zero two\", \"zero point six hundred and two\"],\n[dpformat(0.703, 3), \"zero point seven zero three\", \"zero point seven hundred and three\"],\n[dpformat(0.804, 3), \"zero point eight zero four\", \"zero point eight hundred and four\"],\n[dpformat(0.905, 3), \"zero point nine zero five\", \"zero point nine hundred and five\"]\n )", "description": "", "templateType": "anything", "can_override": false}, "thousandths": {"name": "thousandths", "group": "Ungrouped variables", "definition": "if(len(pron[0][0])=5,dec(pron[0][0])*1000,dec(pron[1][0])*1000)", "description": "", "templateType": "anything", "can_override": false}, "identify": {"name": "identify", "group": "Ungrouped variables", "definition": "if(len(pron[0][0])=5,[[1000,dec(pron[0][0])*1000],[100, dec(pron[1][0])*100]],[[100, dec(pron[0][0])*100],[1000,dec(pron[1][0])*1000]])", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["placedig", "place", "pron", "identify", "thousandths", "hundredths", "pron2"], "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": "

The digit $\\var{placedig}$ in the decimal $\\var{place[0]}$ represents [[0]]

The decimal 0.1 is also known as \"one tenth\" (notice you need ten of them to make a whole).

The decimal 0.01 is also known as \"one hundredth\" (notice you need a hundred of them to make a whole).

The decimal 0.001 is also known as \"one thousandth\" (notice you need a thousand of them to make a whole).

That is, the digit $\\var{placedig}$ in the decimal $\\var{place[0]}$ is in the {place[3]} column and so represents $\\var{placedig}$ {place[3]}.

"}], "gaps": [{"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": "1", "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["

$\\var{placedig}$ {place[1]}

", "

$\\var{placedig}$ {place[2]}

", "

$\\var{placedig}$ {place[3]}

"], "matrix": [0, 0, "1"], "distractors": ["", "", ""]}], "sortAnswers": false}, {"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": "

The decimal $\\var{pron[0][0]}$ should be read as [[0]]

or, as $\\var{identify[0][1]}$ [[1]].

", "stepsPenalty": "2", "steps": [{"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": "

Say each digit individually after the decimal point.

It makes no sense to call 0.500, \"zero point five hundred\" since that sounds a lot bigger than \"zero point five\", or \"zero point fifty\", but these are all equal to the same number! Pronouncing decimals like this is misleading and doesn't help with your intuition. However, this decimal is 500 of something, it is 500 thousandths! But be careful, even reading it that way can be ambiguous when it's read aloud.

That is, $\\var{pron[0][0]}$ is read as {pron[0][1]}.

Alternatively, since the last digit written is in the hundredthsthousandths column, we can think of this (and read it out) as $\\var{identify[0][1]}$ hundredths.thousandths.

"}], "gaps": [{"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": "1", "shuffleChoices": true, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["

zero point {pron[0][1]}

", "

zero point {pron[0][2]}

The decimal $\\var{pron[1][0]}$ should be read as [[0]]

or, as $\\var{identify[1][1]}$ [[1]].

Say each digit individually after the decimal point.

That is, $\\var{pron[1][0]}$ is read as {pron[1][1]}.

Alternatively, since the last digit written is in the hundredthsthousandths column, we can think of this as $\\var{identify[1][1]}$ hundredths.thousandths.

"}], "gaps": [{"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": "1", "shuffleChoices": true, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["

zero point {pron[1][1]}

", "

zero point {pron[1][2]}

"], "matrix": ["1", 0], "distractors": ["", "Please see the steps"]}, {"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["tenths", "hundredths", "thousandths"], "matrix": [0, "if(identify[1][0]=100,1,0)", "if(identify[1][0]=1000,1,0)"], "distractors": ["", "", ""]}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Decimals: common misconceptions", "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/"}], "variable_groups": [], "variables": {"fnzdigbig": {"group": "Ungrouped variables", "description": "", "definition": "random(fnzdigsmall+2..9)", "templateType": "anything", "name": "fnzdigbig"}, "trailshort": {"group": "Ungrouped variables", "description": "", "definition": "random(0.1..0.9#0.1)", "templateType": "anything", "name": "trailshort"}, "fnz": {"group": "Ungrouped variables", "description": "", "definition": "random([[fnzdigsmall/10,fnzdigbig/100,1,0],[fnzdigbig/100,fnzdigsmall/10,0,1]])", "templateType": "anything", "name": "fnz"}, "trail": {"group": "Ungrouped variables", "description": "", "definition": "shuffle(['\\$\\\\var{trailshort}\\$','\\$\\\\var{trailshort}0\\$','\\$\\\\var{trailshort}00\\$','\\$\\\\var{trailshort}000\\$'])[0..2]", "templateType": "anything", "name": "trail"}, "fnzdigsmall": {"group": "Ungrouped variables", "description": "

first non-zero digit

", "definition": "random(1..6)", "templateType": "anything", "name": "fnzdigsmall"}}, "preamble": {"js": "", "css": ""}, "tags": [], "rulesets": {}, "statement": "

Use the drop-down menu to create the correct sentence.

", "ungrouped_variables": ["trail", "trailshort", "fnzdigsmall", "fnzdigbig", "fnz"], "functions": {}, "variablesTest": {"maxRuns": 100, "condition": ""}, "parts": [{"type": "gapfill", "gaps": [{"distractors": ["", "", ""], "type": "1_n_2", "choices": ["greater than", "less than", "equal to"], "displayType": "dropdownlist", "showCorrectAnswer": true, "customMarkingAlgorithm": "", "showCellAnswerState": true, "matrix": [0, 0, "1"], "shuffleChoices": false, "maxMarks": 0, "variableReplacements": [], "unitTests": [], "extendBaseMarkingAlgorithm": true, "marks": 0, "scripts": {}, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "minMarks": 0, "displayColumns": 0}], "sortAnswers": false, "stepsPenalty": "1", "showCorrectAnswer": true, "customMarkingAlgorithm": "", "variableReplacements": [], "steps": [{"type": "information", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "marks": 0, "prompt": "

The trailing zeros do not change the value of a decimal. In the same way that $42$ is no different to $000042$ (regardless of how many zeros are placed at the front), $\\var{trailshort}$ is no different to $\\var{trailshort}0000$ (regardless of how many zeros are placed at the back). This is why it is important to read things such as $0.200$ as \"zero point two zero zero\" and not as \"zero point two hundred\".

In general, the length or number of digits in a decimal does not tell us anything about how big the decimal is. The only things that affect the actual value of a decimal are the non-zero digits and their placement relative to the decimal point (that is their face value and place value).

", "showCorrectAnswer": true, "scripts": {}, "customMarkingAlgorithm": "", "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "unitTests": []}], "prompt": "

The number {trail[0]} is [[0]] {trail[1]}

", "extendBaseMarkingAlgorithm": true, "marks": 0, "scripts": {}, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "unitTests": []}, {"type": "gapfill", "gaps": [{"distractors": ["", "", ""], "type": "1_n_2", "choices": ["greater than", "less than", "equal to"], "displayType": "dropdownlist", "showCorrectAnswer": true, "customMarkingAlgorithm": "", "showCellAnswerState": true, "matrix": ["fnz[2]", "fnz[3]", "0"], "shuffleChoices": false, "maxMarks": 0, "variableReplacements": [], "unitTests": [], "extendBaseMarkingAlgorithm": true, "marks": 0, "scripts": {}, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "minMarks": 0, "displayColumns": 0}], "sortAnswers": false, "stepsPenalty": "1", "showCorrectAnswer": true, "customMarkingAlgorithm": "", "variableReplacements": [], "steps": [{"type": "information", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "marks": 0, "prompt": "

You may have suspected that $\\var{fnz[0]}$ was greater than $\\var{fnz[1]}$ simply because $\\var{fnzdigbig}$ was greater than $\\var{fnzdigsmall}$, however, $\\var{fnzdigbig}$ is in a column with a smaller place value!

You may have suspected that $\\var{fnz[0]}$ was less than $\\var{fnz[1]}$ simply because $\\var{fnzdigsmall}$ was less than $\\var{fnzdigbig}$, however, $\\var{fnzdigsmall}$ is in a column with a larger place value!

In general, the first non-zero digit does not tell us anything about how big the decimal is. The only things that affect the actual value of a decimal are the non-zero digits and their placement relative to the decimal point (that is their face value and place value).

You can add zeros so that the decimals have the same number of decimals places, and then, comparing them might be easier. That is, by appending a zero (which doesn't affect the value) onto the end of $\\var{fnzdigsmall/10}$ it might be clearer that $\\var{fnzdigsmall/10}0$ is greater than $\\var{fnzdigbig/100}$. Note that $\\var{fnzdigsmall/10}0$ is $\\var{fnzdigsmall}0$ hundredths whereas $\\var{fnzdigbig/100}$ is $\\var{fnzdigbig}$ hundredths.

", "showCorrectAnswer": true, "scripts": {}, "customMarkingAlgorithm": "", "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "unitTests": []}], "prompt": "

The number $\\var{fnz[0]}$ is [[0]] $\\var{fnz[1]}$

", "extendBaseMarkingAlgorithm": true, "marks": 0, "scripts": {}, "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "unitTests": []}], "metadata": {"licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International", "description": "

Some students believe a decimal is larger if it is longer, some believe a decimal is larger if its first non-zero digit is larger.

"}, "advice": "

", "type": "question"}, {"name": "Powers of ten", "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/"}], "tags": [], "metadata": {"description": "

Explain powers are repeated multiplication and do some basic squares/cubes. points out how nice powers are ten are because we use a number system based on ten. Explains that 1 followed by n zeroes equals 10^n or viseversa.

Which of the following is the meaning of $\\var{base}^2$

$\\var{base}^2$, read as \"$\\var{base}$ squared\" or \"$\\var{base}$ to the power of two\" means $\\var{base}\\times \\var{base}$. That is, the power counts the number of $\\var{base}$s that are multiplied together.

"}], "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["$\\var{base}\\times 2$", "$\\var{base}\\times \\var{base}$", "$\\var{base}+\\var{base}$", "$\\var{base}2$"], "matrix": [0, "1", 0, 0], "distractors": ["", "", "", ""]}, {"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": "

$10^\\var{power1}=$[[0]]

Input the result of the calculation without using a calculator.

", "stepsPenalty": "3", "steps": [{"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": "

$10^\\var{power1}$ means there are $\\var{power1}$ tens all multiplied together. These are referred to as \"powers of ten\". Here are some examples:

$\\begin{align*}10^1&=10\\\\10^2&=100\\\\10^3&=1\\,000\\\\10^4&=10\\,000\\\\10^5&=100\\,000\\\\10^6&=1\\,000\\,000\\\\\\end{align*}$

Notice that every extra power of ten results in an extra zero. This is because our number system is based on the number ten (we can say it is a base-ten system or a decimal number system) which means each 'column' has a place value ten times bigger than the 'column' to the right of it. Because of this, multiplying by ten moves the decimal point to the right in order to make the number bigger (or we can think of the digits all moving up to the next column to the left).

In general, for a counting number $n$, the result of $10^n$ is the number written as \"1\" followed by $n$ zeros. Conversely, the number written as \"1\" followed by $n$ zeros is equal to $10^n$.

$10^\\var{power2}$ would equal the number written $1$ followed by how many zeroes? [[0]]

$10^\\var{power2}$ means there are $\\var{power2}$ tens all multiplied together. These are referred to as \"powers of ten\". Here are some examples:

$\\begin{align*}10^1&=10\\\\10^2&=100\\\\10^3&=1\\,000\\\\10^4&=10\\,000\\\\10^5&=100\\,000\\\\10^6&=1\\,000\\,000\\\\\\end{align*}$

In general, for a counting number $n$, the result of $10^n$ is the number written as \"1\" followed by $n$ zeros. Conversely, the number written as \"1\" followed by $n$ zeros is equal to $10^n$.

The digit \"1\" followed by $\\var{power3}$ zeros, that is, $\\var{10^power3}$ is $10$ to the power of [[0]].

$10^\\var{power3}$ means there are $\\var{power3}$ tens all multiplied together, which results in a \"1\" followed by $\\var{power3}$ zeros. These are referred to as \"powers of ten\". Here are some examples:

$\\begin{align*}10^1&=10\\\\10^2&=100\\\\10^3&=1\\,000\\\\10^4&=10\\,000\\\\10^5&=100\\,000\\\\10^6&=1\\,000\\,000\\\\\\end{align*}$

In general, for a counting number $n$, the result of $10^n$ is the number written as \"1\" followed by $n$ zeros. Conversely, the number written as \"1\" followed by $n$ zeros is equal to $10^n$.

Write the following question down on paper and evaluate it without using a calculator.

", "variablesTest": {"condition": "", "maxRuns": 100}, "variable_groups": [], "parts": [{"showFeedbackIcon": true, "gaps": [{"showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "variableReplacements": [], "type": "numberentry", "customMarkingAlgorithm": "", "showCorrectAnswer": true, "marks": 1, "variableReplacementStrategy": "originalfirst", "mustBeReducedPC": 0, "allowFractions": false, "mustBeReduced": false, "scripts": {}, "correctAnswerStyle": "plain", "minValue": "ans1", "unitTests": [], "maxValue": "ans1", "extendBaseMarkingAlgorithm": true}], "variableReplacements": [], "type": "gapfill", "customMarkingAlgorithm": "", "showCorrectAnswer": true, "marks": 0, "variableReplacementStrategy": "originalfirst", "stepsPenalty": "1", "steps": [{"showFeedbackIcon": true, "unitTests": [], "customMarkingAlgorithm": "", "prompt": "

$\\var{poweroften[0]}$ has {pronpower[0]} $0$s after the leading $1$. This means to evaluate $\\var{dec1}\\times \\var{poweroften[0]}$ we just move the decimal point in $\\var{dec1}$ {pronpower[0]} decimal places to the right (to make the decimal $\\var{poweroften[0]}$ times bigger) and get $\\var{ans1}$.

", "scripts": {}, "variableReplacementStrategy": "originalfirst", "type": "information", "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "marks": 0, "variableReplacements": []}], "scripts": {}, "unitTests": [], "sortAnswers": false, "prompt": "

$\\var{dec1}\\times \\var{poweroften[0]}=$ [[0]]

", "extendBaseMarkingAlgorithm": true}, {"showFeedbackIcon": true, "gaps": [{"showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "variableReplacements": [], "type": "numberentry", "customMarkingAlgorithm": "", "showCorrectAnswer": true, "marks": 1, "variableReplacementStrategy": "originalfirst", "mustBeReducedPC": 0, "allowFractions": false, "mustBeReduced": false, "scripts": {}, "correctAnswerStyle": "plain", "minValue": "ans2", "unitTests": [], "maxValue": "ans2", "extendBaseMarkingAlgorithm": true}], "variableReplacements": [], "type": "gapfill", "customMarkingAlgorithm": "", "showCorrectAnswer": true, "marks": 0, "variableReplacementStrategy": "originalfirst", "stepsPenalty": "1", "steps": [{"showFeedbackIcon": true, "unitTests": [], "customMarkingAlgorithm": "", "prompt": "

$\\var{poweroften[1]}$ has {pronpower[1]} $0$s after the leading $1$. This means to evaluate $\\var{dec2}\\times \\var{poweroften[1]}$ we just move the decimal point in $\\var{dec2}$ {pronpower[1]} decimal places to the right (to make the decimal $\\var{poweroften[1]}$ times bigger) and get $\\var{ans2}$.

$\\var{dec2}\\times\\var{poweroften[1]}=$ [[0]]

", "extendBaseMarkingAlgorithm": true}, {"showFeedbackIcon": true, "gaps": [{"showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "variableReplacements": [], "type": "numberentry", "customMarkingAlgorithm": "", "showCorrectAnswer": true, "marks": 1, "variableReplacementStrategy": "originalfirst", "mustBeReducedPC": 0, "allowFractions": false, "mustBeReduced": false, "scripts": {}, "correctAnswerStyle": "plain", "minValue": "ans3", "unitTests": [], "maxValue": "ans3", "extendBaseMarkingAlgorithm": true}], "variableReplacements": [], "type": "gapfill", "customMarkingAlgorithm": "", "showCorrectAnswer": true, "marks": 0, "variableReplacementStrategy": "originalfirst", "stepsPenalty": "1", "steps": [{"showFeedbackIcon": true, "unitTests": [], "customMarkingAlgorithm": "", "prompt": "

$\\var{poweroften[2]}$ has {pronpower[2]} $0$s after the leading $1$. This means to evaluate $\\var{dec3}\\div \\var{poweroften[2]}$ we just move the decimal point in $\\var{dec3}$ {pronpower[2]} decimal places to the left (to make the decimal smaller) and get $\\var{ans3}$.

$\\var{dec3}\\div\\var{poweroften[2]}=$ [[0]]

", "extendBaseMarkingAlgorithm": true}, {"showFeedbackIcon": true, "gaps": [{"showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "variableReplacements": [], "type": "numberentry", "customMarkingAlgorithm": "", "showCorrectAnswer": true, "marks": 1, "variableReplacementStrategy": "originalfirst", "mustBeReducedPC": 0, "allowFractions": false, "mustBeReduced": false, "scripts": {}, "correctAnswerStyle": "plain", "minValue": "ans4", "unitTests": [], "maxValue": "ans4", "extendBaseMarkingAlgorithm": true}], "variableReplacements": [], "type": "gapfill", "customMarkingAlgorithm": "", "showCorrectAnswer": true, "marks": 0, "variableReplacementStrategy": "originalfirst", "stepsPenalty": "1", "steps": [{"showFeedbackIcon": true, "unitTests": [], "customMarkingAlgorithm": "", "prompt": "

Recall, the fraction bar simply denotes division.

$\\var{poweroften[3]}$ has {pronpower[3]} $0$s after the leading $1$. This means to evaluate $\\var{dec4}\\div \\var{poweroften[3]}$ we just move the decimal point in $\\var{dec4}$ {pronpower[3]} decimal places to the left (to make the decimal smaller) and get $\\var{ans4}$.

$\\displaystyle \\frac{\\var{dec4}}{\\var{poweroften[3]}}=$ [[0]]

", "extendBaseMarkingAlgorithm": true}], "ungrouped_variables": ["dec1", "dec2", "dec3", "dec4", "power", "poweroften", "ans1", "ans2", "ans3", "ans4", "pronpower"], "rulesets": {}, "preamble": {"js": "", "css": ""}, "tags": [], "metadata": {"licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International", "description": "

By powers of ten I mean a 1 followed by some 0s. The scientific notation questions will take care of the power of ten notation.

"}, "functions": {}, "advice": "

Multiplying or dividing by a power of ten (such as a $1$ followed by some $0$s) moves the decimal point. Multiplying moves the decimal point to make the number bigger (that is, to the right). Dividing moves the decimal to make the number smaller (that is, to the left). The number of $0$s indicates the number of places you should move the decimal place.

", "variables": {"ans4": {"name": "ans4", "description": "", "group": "Ungrouped variables", "definition": "dec4/poweroften[3]", "templateType": "anything"}, "dec4": {"name": "dec4", "description": "", "group": "Ungrouped variables", "definition": "random(list(0.111..0.499#0.001))", "templateType": "anything"}, "ans3": {"name": "ans3", "description": "

ans3

", "group": "Ungrouped variables", "definition": "dec3/poweroften[2]", "templateType": "anything"}, "dec1": {"name": "dec1", "description": "", "group": "Ungrouped variables", "definition": "random(list(0.111..0.999#0.001))*10", "templateType": "anything"}, "ans1": {"name": "ans1", "description": "", "group": "Ungrouped variables", "definition": "dec1*poweroften[0]", "templateType": "anything"}, "poweroften": {"name": "poweroften", "description": "", "group": "Ungrouped variables", "definition": "map(10^n,n,power)", "templateType": "anything"}, "power": {"name": "power", "description": "", "group": "Ungrouped variables", "definition": "shuffle([1,2,3,4])", "templateType": "anything"}, "pronpower": {"name": "pronpower", "description": "", "group": "Ungrouped variables", "definition": "[switch(power[0]=2,'two',power[0]=3,'three',power[0]=4,'four','one'),switch(power[1]=2,'two',power[1]=3,'three',power[1]=4,'four','one'),switch(power[2]=2,'two',power[2]=3,'three',power[2]=4,'four','one'),switch(power[3]=2,'two',power[3]=3,'three',power[3]=4,'four','one')]", "templateType": "anything"}, "dec2": {"name": "dec2", "description": "", "group": "Ungrouped variables", "definition": "random(list(0.011..0.099#0.0001))", "templateType": "anything"}, "dec3": {"name": "dec3", "description": "", "group": "Ungrouped variables", "definition": "random(list(0.500..0.999#0.001))*10", "templateType": "anything"}, "ans2": {"name": "ans2", "description": "", "group": "Ungrouped variables", "definition": "dec2*poweroften[1]", "templateType": "anything"}}, "type": "question"}, {"name": "Rounding to 0, 1, 2 or 3 decimal places", "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/"}], "tags": [], "metadata": {"description": "

Round random numbers to the closest whole number, 1, 2 or 3 decimals places.

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"trick": {"name": "trick", "group": "Ungrouped variables", "definition": "random(0.04,0.05, 0.06, 0.07, 0.08)", "description": "", "templateType": "anything", "can_override": false}, "number2": {"name": "number2", "group": "Ungrouped variables", "definition": "random(10.001..300#0.0003)", "description": "", "templateType": "anything", "can_override": false}, "ans": {"name": "ans", "group": "Ungrouped variables", "definition": "precround(number,ndp)", "description": "", "templateType": "anything", "can_override": false}, "digit_to_the_right": {"name": "digit_to_the_right", "group": "Ungrouped variables", "definition": "mod(floor(10^(ndp+1)*number),10)\n", "description": "", "templateType": "anything", "can_override": false}, "number": {"name": "number", "group": "Ungrouped variables", "definition": "random(10.00001..90#0.00002)", "description": "", "templateType": "anything", "can_override": false}, "n4r": {"name": "n4r", "group": "Ungrouped variables", "definition": "random(0.001..0.999#0.001)", "description": "", "templateType": "anything", "can_override": false}, "seed": {"name": "seed", "group": "Ungrouped variables", "definition": "random(1,0.1,0.01,0.001)", "description": "", "templateType": "anything", "can_override": false}, "ndp": {"name": "ndp", "group": "Ungrouped variables", "definition": "countdp(string(seed))", "description": "", "templateType": "anything", "can_override": false}, "direction": {"name": "direction", "group": "Ungrouped variables", "definition": "if(digit_to_the_right<5,'down', 'up')", "description": "", "templateType": "anything", "can_override": false}, "less_greater": {"name": "less_greater", "group": "Ungrouped variables", "definition": "if(digit_to_the_right<5,'less than', 'greater than or equal to')", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["seed", "ndp", "number", "digit_to_the_right", "ans", "direction", "less_greater", "number2", "trick", "n4r"], "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": "

$\\var{number}$ rounded to the nearest whole number {ndp} decimal place {ndp} decimal places is [[0]].

When we are rounding we look at the first digit that we might discard. If it is $5$ or greater we round up. If it is less than $5$ we round down.

We want to round to the nearest whole number {ndp} decimal place {ndp} decimal places. The digit to the right is $\\var{digit_to_the_right}$, which is {less_greater} $5$ so we round {direction} to $\\var{ans}$

A single question which asks you to round to the nearest ten, hundred or thousand.

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"number": {"name": "number", "group": "Ungrouped variables", "definition": "random(10*seed..50*seed except 10*seed..50*seed#seed)", "description": "", "templateType": "anything", "can_override": false}, "ans": {"name": "ans", "group": "Ungrouped variables", "definition": "tonearest(number, seed)\n", "description": "", "templateType": "anything", "can_override": false}, "digit_to_the_right": {"name": "digit_to_the_right", "group": "Ungrouped variables", "definition": "mod(floor(10*number/seed),10)\n//(mod(number,seed)-mod(number, seed/10))/(seed/10)\n//floor(lastdigits/(seed/10))", "description": "", "templateType": "anything", "can_override": false}, "seed": {"name": "seed", "group": "Ungrouped variables", "definition": "random(10,100,1000)", "description": "", "templateType": "anything", "can_override": false}, "direction": {"name": "direction", "group": "Ungrouped variables", "definition": "if(digit_to_the_right<5,'down', 'up')", "description": "", "templateType": "anything", "can_override": false}, "seedtext": {"name": "seedtext", "group": "Ungrouped variables", "definition": "switch(seed=10, 'ten', seed=100, 'hundred', seed=1000, 'thousand', 'error')", "description": "", "templateType": "anything", "can_override": false}, "less_greater": {"name": "less_greater", "group": "Ungrouped variables", "definition": "if(digit_to_the_right<5,'less than', 'greater than or equal to')", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["seed", "seedtext", "number", "digit_to_the_right", "direction", "less_greater", "ans"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

$\\var{number}$ rounded to the nearest {seedtext} is [[0]].

When we are rounding we look at the first digit that we might discard. If it is $5$ or greater we round up. If it is less than $5$ we round down.

To round $\\var{number}$ to the nearest {seedtext}, we look to the right of the {seedtext}s column and see the digit $\\var{digit_to_the_right}$.

Since $\\var{digit_to_the_right}$ is {less_greater} $5$ we round {direction} to $\\var{ans}$.

"}], "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "ans", "maxValue": "ans", "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"}]}], "allowPrinting": true, "navigation": {"allowregen": true, "reverse": true, "browse": true, "allowsteps": true, "showfrontpage": false, "showresultspage": "oncompletion", "navigatemode": "sequence", "onleave": {"action": "none", "message": ""}, "preventleave": true, "startpassword": ""}, "timing": {"allowPause": true, "timeout": {"action": "none", "message": ""}, "timedwarning": {"action": "none", "message": ""}}, "feedback": {"showactualmark": true, "showtotalmark": true, "showanswerstate": true, "allowrevealanswer": true, "advicethreshold": 0, "intro": "", "end_message": "", "reviewshowscore": true, "reviewshowfeedback": true, "reviewshowexpectedanswer": true, "reviewshowadvice": true, "feedbackmessages": []}, "diagnostic": {"knowledge_graph": {"topics": [], "learning_objectives": []}, "script": "diagnosys", "customScript": ""}, "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}], "extensions": [], "custom_part_types": [], "resources": []}