No advice included.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "", "advice": "a) Say each digit individually after the decimal point.
\nIt makes no sense to call 0.500, \"zero point five hundred\" since that sounds a lot bigger than \"zero
So, for this question, $\\var{pron[0]}$ is read as {pron[1]}.
\n\nb) The decimal 0.1 is also known as \"one tenth\" (notice you need ten of them to make a whole).
\nThe decimal 0.01 is also known as \"one hundredth\" (notice you need a hundred of them to make a whole).
\nThe decimal 0.001 is also known as \"one thousandth\" (notice you need a thousand of them to make a whole).
\nSo, for this question we say the digit $\\var{placedig}$ in the decimal $\\var{place[0]}$ represents $\\var{placedig}$ {place[3]}.
", "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": "random(\n[dpformat(0.10, 2), \"zero point one zero\", \"zero point ten\"], \n[dpformat(0.11, 2), \"zero point one one\", \"zero point eleven\"], \n[dpformat(0.12, 2), \"zero point one two\", \"zero point twelve\"],\n[dpformat(0.13, 2), \"zero point one three\", \"zero point thirteen\"],\n[dpformat(0.14, 2), \"zero point one four\", \"zero point fourteen\"],\n[dpformat(0.15, 2), \"zero point one five\", \"zero point fifteen\"],\n[dpformat(0.16, 2), \"zero point one six\", \"zero point sixteen\"],\n[dpformat(0.17, 2), \"zero point one seven\", \"zero point seventeen\"],\n[dpformat(0.18, 2), \"zero point one eight\", \"zero point eighteen\"],\n[dpformat(0.19, 2), \"zero point one nine\", \"zero point ninteen\"], \n\n[dpformat(0.20, 2), \"zero point two zero\", \"zero point twenty\"], \n[dpformat(0.21, 2), \"zero point two one\", \"zero point twenty one\"], \n[dpformat(0.22, 2), \"zero point two two\", \"zero point twenty two\"],\n[dpformat(0.23, 2), \"zero point two three\", \"zero point twenty three\"],\n[dpformat(0.24, 2), \"zero point two four\", \"zero point twenty four\"], \n[dpformat(0.25, 2), \"zero point two five\", \"zero point twenty five\"],\n[dpformat(0.26, 2), \"zero point two six\", \"zero point twenty six\"],\n[dpformat(0.27, 2), \"zero point two seven\", \"zero point twenty seven\"],\n[dpformat(0.28, 2), \"zero point two eight\", \"zero point twenty eight\"],\n[dpformat(0.29, 2), \"zero point two nine\", \"zero point twenty nine\"], \n \n[dpformat(0.30, 2), \"zero point three zero\", \"zero point thirty\"], \n[dpformat(0.31, 2), \"zero point three one\", \"zero point thirty one\"], \n[dpformat(0.32, 2), \"zero point three two\", \"zero point thirty two\"],\n[dpformat(0.33, 2), \"zero point three three\", \"zero point thirty three\"],\n[dpformat(0.34, 2), \"zero point three four\", \"zero point thirty four\"], \n[dpformat(0.35, 2), \"zero point three five\", \"zero point thirty five\"],\n[dpformat(0.36, 2), \"zero point three six\", \"zero point thirty six\"],\n[dpformat(0.37, 2), \"zero point three seven\", \"zero point thirty seven\"],\n[dpformat(0.38, 2), \"zero point three eight\", \"zero point thirty eight\"],\n[dpformat(0.39, 2), \"zero point three nine\", \"zero point thirty nine\"], \n \n[dpformat(0.40, 2), \"zero point four zero\", \"zero point forty\"], \n[dpformat(0.41, 2), \"zero point four one\", \"zero point forty one\"], \n[dpformat(0.42, 2), \"zero point four two\", \"zero point forty two\"],\n[dpformat(0.43, 2), \"zero point four three\", \"zero point forty three\"],\n[dpformat(0.44, 2), \"zero point four four\", \"zero point forty four\"], \n[dpformat(0.45, 2), \"zero point four five\", \"zero point forty five\"],\n[dpformat(0.46, 2), \"zero point four six\", \"zero point forty six\"],\n[dpformat(0.47, 2), \"zero point four seven\", \"zero point forty seven\"],\n[dpformat(0.48, 2), \"zero point four eight\", \"zero point forty eight\"],\n[dpformat(0.49, 2), \"zero point four nine\", \"zero point forty nine\"], \n \n[dpformat(0.50, 2), \"zero point five zero\", \"zero point fifty\"], \n[dpformat(0.51, 2), \"zero point five one\", \"zero point fifty one\"], \n[dpformat(0.52, 2), \"zero point five two\", \"zero point fifty two\"],\n[dpformat(0.53, 2), \"zero point five three\", \"zero point fifty three\"],\n[dpformat(0.54, 2), \"zero point five four\", \"zero point fifty four\"], \n[dpformat(0.55, 2), \"zero point five five\", \"zero point fifty five\"],\n[dpformat(0.56, 2), \"zero point five six\", \"zero point fifty six\"],\n[dpformat(0.57, 2), \"zero point five seven\", \"zero point fifty seven\"],\n[dpformat(0.58, 2), \"zero point five eight\", \"zero point fifty eight\"],\n[dpformat(0.59, 2), \"zero point five nine\", \"zero point fifty nine\"], \n \n[0.60, \"zero point six zero\", \"zero point sixty\"], \n\n\n[0.70, \"zero point seven zero\", \"zero point seventy\"], \n \n\n[0.80, \"zero point eight zero\", \"zero point eighty\"], \n\n \n[0.90, \"zero point nine zero\", \"zero point ninety\"], \n\n \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)", "description": "", "templateType": "anything", "can_override": false}, "placedig": {"name": "placedig", "group": "Ungrouped variables", "definition": "random(1..9)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["pron", "placedig", "place"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"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, "prompt": "The decimal $\\var{pron[0]}$ should be read as
", "minMarks": 0, "maxMarks": "1", "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["{pron[1]}
", "{pron[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, "prompt": "The digit $\\var{placedig}$ in the decimal $\\var{place[0]}$ represents
", "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": ["", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Compare decimals", "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": "Lyn Armstrong", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2012/"}, {"name": "Susan McGlynn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2148/"}, {"name": "Shatha Aziz", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/12378/"}], "tags": [], "metadata": {"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 included.
Complete the following without using a calculator.
\nUse the drop-down menu to create the correct sentence.
", "advice": "a) 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
In general, the length or number of digits in
b)
\nYou 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!
\nYou 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!
\nIn 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).
\nYou 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.
", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"fnzdigbig": {"name": "fnzdigbig", "group": "Ungrouped variables", "definition": "random(fnzdigsmall+2..9)", "description": "", "templateType": "anything", "can_override": false}, "trailshort": {"name": "trailshort", "group": "Ungrouped variables", "definition": "random(0.1..0.9#0.1)", "description": "", "templateType": "anything", "can_override": false}, "fnz": {"name": "fnz", "group": "Ungrouped variables", "definition": "random([[fnzdigsmall/10,fnzdigbig/100,1,0],[fnzdigbig/100,fnzdigsmall/10,0,1]])", "description": "", "templateType": "anything", "can_override": false}, "trail": {"name": "trail", "group": "Ungrouped variables", "definition": "shuffle(['\\$\\\\var{trailshort}\\$','\\$\\\\var{trailshort}0\\$','\\$\\\\var{trailshort}00\\$','\\$\\\\var{trailshort}000\\$'])[0..2]", "description": "", "templateType": "anything", "can_override": false}, "fnzdigsmall": {"name": "fnzdigsmall", "group": "Ungrouped variables", "definition": "random(1..6)", "description": "first non-zero digit
", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["trail", "trailshort", "fnzdigsmall", "fnzdigbig", "fnz"], "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 {trail[0]} is [[0]] {trail[1]}
", "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": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["greater than", "less than", "equal to"], "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 number $\\var{fnz[0]}$ is [[0]] $\\var{fnz[1]}$
", "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": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["greater than", "less than", "equal to"], "matrix": ["fnz[2]", "fnz[3]", "0"], "distractors": ["", "", ""]}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Multiply and divide a decimal by a power of 10", "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": "Don Shearman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/680/"}, {"name": "Jim Pettigrew", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2037/"}, {"name": "Susan McGlynn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2148/"}], "tags": [], "metadata": {"description": "Advice included.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "Complete the following without using a calculator.
", "advice": "a) $\\var{poweroften[0]}$ 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 $\\var{ans1}$.
\nb) $\\var{poweroften[1]}$ 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 $\\var{ans2}$.
\nc) $\\var{poweroften[2]}$ 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 $\\var{ans3}$.
\nd) Recall, the fraction bar simply denotes division.
\n$\\var{poweroften[3]}$ 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 $\\var{ans4}$.
", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"ans4": {"name": "ans4", "group": "Ungrouped variables", "definition": "siground(dec4/poweroften[3],3)", "description": "", "templateType": "anything", "can_override": false}, "dec4": {"name": "dec4", "group": "Ungrouped variables", "definition": "random(list(0.111..0.499#0.001))", "description": "", "templateType": "anything", "can_override": false}, "ans3": {"name": "ans3", "group": "Ungrouped variables", "definition": "siground(dec3/poweroften[2],3)", "description": "ans3
", "templateType": "anything", "can_override": false}, "dec1": {"name": "dec1", "group": "Ungrouped variables", "definition": "random(list(0.111..0.999#0.001))*10", "description": "", "templateType": "anything", "can_override": false}, "ans1": {"name": "ans1", "group": "Ungrouped variables", "definition": "siground(dec1*poweroften[0],3)", "description": "", "templateType": "anything", "can_override": false}, "poweroften": {"name": "poweroften", "group": "Ungrouped variables", "definition": "map(10^n,n,power)", "description": "", "templateType": "anything", "can_override": false}, "power": {"name": "power", "group": "Ungrouped variables", "definition": "shuffle([1,2,3,4])", "description": "", "templateType": "anything", "can_override": false}, "pronpower": {"name": "pronpower", "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')]", "description": "", "templateType": "anything", "can_override": false}, "dec2": {"name": "dec2", "group": "Ungrouped variables", "definition": "random(list(0.011..0.099#0.0001))", "description": "", "templateType": "anything", "can_override": false}, "dec3": {"name": "dec3", "group": "Ungrouped variables", "definition": "random(list(0.500..0.999#0.001))*10", "description": "", "templateType": "anything", "can_override": false}, "ans2": {"name": "ans2", "group": "Ungrouped variables", "definition": "siground(dec2*poweroften[1],3)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["dec1", "dec2", "dec3", "dec4", "power", "poweroften", "ans1", "ans2", "ans3", "ans4", "pronpower"], "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": "$\\var{dec1}\\times \\var{poweroften[0]}=$ [[0]]
\n", "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": "ans1", "maxValue": "ans1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "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": "$\\var{dec2}\\times\\var{poweroften[1]}=$ [[0]]
\n", "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": "ans2", "maxValue": "ans2", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "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": "$\\var{dec3}\\div\\var{poweroften[2]}=$ [[0]]
\n", "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": "ans3", "maxValue": "ans3", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "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": "$\\displaystyle \\frac{\\var{dec4}}{\\var{poweroften[3]}}=$ [[0]]
", "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": "ans4", "maxValue": "ans4", "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": "Rename a fraction in decimal form", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Susan McGlynn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2148/"}], "tags": [], "metadata": {"description": "Four parts, each converting a fraction to a decimal. Denominators are: a (factors of 100), b (8), c (3) and d (%, fraction out of 100, fraction in simplest form). No advice included.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "Complete the following without using a calculator.
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\n$\\frac{\\var{a}}{\\var{b}}$
", "minValue": "a/b", "maxValue": "a/b", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"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, "prompt": "Rewrite the following in decimal form.
\n$\\frac{\\var{x}}{8}$
", "minValue": "x/8", "maxValue": "x/8", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "3", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"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, "prompt": "Rewrite the following in decimal form.
\n$\\frac{\\var{y}}{3}$
", "minValue": "y/3", "maxValue": "y/3", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "3", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"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": "Fill in the gap to complete the table below.
\n\n| simplest fraction | \nhundredths | \ndecimal | \npercentage | \n
| $\\frac{3}{4}$ | \n$\\frac{75}{100}$ | \n$0.75$ | \n$75\\%$ | \n
| $\\frac{4}{50}$ | \n$\\frac{8}{100}$ | \n[[0]] | \n$8\\%$ | \n
| $\\frac{3}{20}$ | \n$\\frac{15}{100}$ | \n$0.15$ | \n$15\\%$ | \n
| $\\frac{27}{20}$ | \n$\\frac{135}{100}$ | \n$1.35$ | \n$135\\%$ | \n
Decimals addition algorithm. 2 and 3 digit numbers. Carrying.
\nShow steps.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "Evaluate the following without using a calculator.
\n", "advice": "Write the following question down on paper and evaluate it without using a calculator.
\nIf 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.
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\n", "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": "Generally we set up $\\var{threedigit1}+\\var{threedigit2}$ with the decimal points lined up vertically so that the columns with the same place value are also lined up vertically:
\n| $0$ | \n. | \n$\\var{cdigs[2]}$ | \n$\\var{cdigs[1]}$ | \n\n | $+$ | \n
| $0$ | \n. | \n$\\var{cdigs[5]}$ | \n$\\var{cdigs[4]}$ | \n$\\var{cdigs[3]}$ | \n\n |
| \n | \n | \n | $\\phantom{0}$ | \n\n | \n |
Note that we can pad out the decimal with zeros if we prefer:
\n| $0$ | \n. | \n$\\var{cdigs[2]}$ | \n$\\var{cdigs[1]}$ | \n$\\color{red}{\\var{cdigs[0]}}$ | \n$+$ | \n
| $0$ | \n. | \n$\\var{cdigs[5]}$ | \n$\\var{cdigs[4]}$ | \n$\\var{cdigs[3]}$ | \n\n |
| \n | \n | \n | $\\phantom{0}$ | \n\n | \n |
Now we add the digits in the column to the far right (in this case, the thousandths column).
\nThis results in $\\var{cunitsum}$ and so we place $\\var{cunitsumlastdigit}$ under the line in this column.
\nThis results in $\\var{cunitsum}$ and so we place $\\var{cunitsumlastdigit}$ under the line in this column and carry the $1$ into the next column to the left.
\n| $\\overset{\\phantom{1}}{0}$ | \n. | \n$\\overset{\\phantom{1}}{\\var{cdigs[2]}}$ | \n$\\overset{\\color{red}1}{\\var{cdigs[1]}}$ $\\overset{\\phantom{0}}{\\var{cdigs[1]}}$ | \n$\\color{green}{\\overset{\\phantom{1}}{\\var{cdigs[0]}}}$ | \n$+$ | \n
| $0$ | \n. | \n$\\var{cdigs[5]}$ | \n$\\var{cdigs[4]}$ | \n$\\color{green}{\\var{cdigs[3]}}$ | \n\n |
| \n | \n | \n | \n | $\\color{red}{\\var{cunitSumLastDigit}}$ | \n\n |
Now we add the digits in the next column to the left (in this case, the hundredths column).
\nThis results in $\\var{ctenSum}$ and so we place $\\var{ctenSumlastdigit}$ under the line in this column.
\nThis results in $\\var{ctenSum}$ and so we place $\\var{ctenSumlastdigit}$ under the line in this column and carry the $1$ into the next column to the left.
\n| $\\overset{\\phantom{1}}{0}$ | \n. | \n$\\overset{\\color{red}{1}}{\\var{cdigs[2]}}$ $\\overset{\\phantom{1}}{\\var{cdigs[2]}}$ | \n$\\color{green}{\\overset{1}{\\var{cdigs[1]}}}$ $\\color{green}{\\overset{\\phantom{0}}{\\var{cdigs[1]}}}$ | \n$\\overset{\\phantom{1}}{\\var{cdigs[0]}}$ | \n$+$ | \n
| $0$ | \n. | \n$\\var{cdigs[5]}$ | \n$\\color{green}{\\var{cdigs[4]}}$ | \n$\\var{cdigs[3]}$ | \n\n |
| \n | \n | \n | $\\color{red}{\\var{ctenSumlastdigit}}$ | \n${\\var{cunitSumLastDigit}}$ | \n\n |
Now we add the digits in the next column to the left (in this case, the tenths column).
\nThis is $\\var{chunsum}$ so we place $\\var{chunsum}$ under the line in this column.
\nThis is $\\var{chunsum}$ so we place $\\var{chunsumlastdigit}$ under the line in this column and carry $\\var{chuncarry}$ into the next column to the left (which in this case is the ones column on the other side of the decimal point).
\n| $\\overset{\\color{red}1}{0}$ $\\overset{\\phantom{1}}{0}$ | \n. | \n$\\color{green}{\\overset{1}{\\var{cdigs[2]}}}$ $\\color{green}{\\overset{\\phantom{1}}{\\var{cdigs[2]}}}$ | \n$\\overset{1}{\\var{cdigs[1]}}$ $\\overset{\\phantom{0}}{\\var{cdigs[1]}}$ | \n$\\overset{\\phantom{1}}{\\var{cdigs[0]}}$ | \n$+$ | \n
| $0$ | \n. | \n$\\color{green}{\\var{cdigs[5]}}$ | \n$\\var{cdigs[4]}$ | \n$\\var{cdigs[3]}$ | \n\n |
| \n | . | \n$\\color{red}{\\var{chunsumlastdigit}}$ | \n$\\var{ctenSumlastdigit}$ | \n${\\var{cunitSumLastDigit}}$ | \n\n |
Now we add the digits in the next column to the left (in this case, the ones column).
\nThis is just $0$ so we place $0$ under the line in this column.
\nThis is just $\\var{chuncarry}$ so we place $\\var{chuncarry}$ under the line in this column.
\n| $\\color{green}{\\overset{1}{0}}$ $\\color{green}{\\overset{\\phantom{1}}{0}}$ | \n. | \n$\\overset{1}{\\var{cdigs[2]}}$ $\\overset{\\phantom{1}}{\\var{cdigs[2]}}$ | \n$\\overset{1}{\\var{cdigs[1]}}$ $\\overset{\\phantom{0}}{\\var{cdigs[1]}}$ | \n$\\overset{\\phantom{1}}{\\var{cdigs[0]}}$ | \n$+$ | \n
| $\\color{green}{0}$ | \n. | \n$\\var{cdigs[5]}$ | \n$\\var{cdigs[4]}$ | \n$\\var{cdigs[3]}$ | \n\n |
| $\\color{red}{\\var{chuncarry}}$ | \n. | \n$\\var{chunsumlastdigit}$ | \n$\\var{ctenSumlastdigit}$ | \n${\\var{cunitSumLastDigit}}$ | \n\n |
The answer is therefore $\\var{cans}$.
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", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "Evaluate the following without using a calculator.
", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"num4": {"name": "num4", "group": "Ungrouped variables", "definition": "random(1..3)+random(1..3)/10 +random(1..5)/100", "description": "", "templateType": "anything", "can_override": false}, "num5": {"name": "num5", "group": "Ungrouped variables", "definition": "random(6..9)+random(1..5)/100 +random(1..5)/1000", "description": "", "templateType": "anything", "can_override": false}, "num6": {"name": "num6", "group": "Ungrouped variables", "definition": "random(1..5)+random(1..5)/100 +random(1..5)/1000", "description": "", "templateType": "anything", "can_override": false}, "num7": {"name": "num7", "group": "Ungrouped variables", "definition": " random(5..9)+random(1..5)/10 +random(1..5)/100", "description": "", "templateType": "anything", "can_override": false}, "num1": {"name": "num1", "group": "Ungrouped variables", "definition": "random(4..7)+random(4..7)/10 ", "description": "", "templateType": "anything", "can_override": false}, "num2": {"name": "num2", "group": "Ungrouped variables", "definition": "num1-random(1..3)+random(1..3)/10", "description": "", "templateType": "anything", "can_override": false}, "num3": {"name": "num3", "group": "Ungrouped variables", "definition": "random(4..5)+random(1..5)/10 +random(1..5)/100", "description": "", "templateType": "anything", "can_override": false}, "ans1": {"name": "ans1", "group": "Ungrouped variables", "definition": "num1-num2", "description": "", "templateType": "anything", "can_override": false}, "ans2": {"name": "ans2", "group": "Ungrouped variables", "definition": "num3-num4", "description": "", "templateType": "anything", "can_override": false}, "ans3": {"name": "ans3", "group": "Ungrouped variables", "definition": "num5-num6", "description": "", "templateType": "anything", "can_override": false}, "num8": {"name": "num8", "group": "Ungrouped variables", "definition": "random(1..4)+random(1..5)/10 +random(1..5)/100+random(1..5)/1000", "description": "", "templateType": "anything", "can_override": false}, "ans4": {"name": "ans4", "group": "Ungrouped variables", "definition": "num7-num8", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["num1", "num2", "ans1", "num3", "num4", "ans2", "num5", "num6", "ans3", "num7", "num8", "ans4"], "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": "What's $\\var{num1} - \\var{num2} $?
\nPlease give your answer with exactly 1 decimal place.
\nAnswer: $\\var{num1} - \\var{num2} =$ [[0]]
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\nPlease give your answer with exactly 2 decimal places.
\nAnswer: $\\var{num3} - \\var{num4} =$ [[0]]
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\nb) Multiplying decimals requiring the multiplication algorithm.
\nAdvice included.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "Complete the following without using a calculator.
", "advice": "a) Remove the decimal points, do the multiplication of whole numbers, then put the decimal place in the answer so that the number of decimal places in the question and the answer are the same.
\n\n
That is,
\nand therefore $\\var{easy1}\\times\\var{easy2}=\\var{easyans}0$. But note, we don't need to write the last zero so we could also write $\\var{easy1}\\times\\var{easy2}=\\var{easyans}$.
\nand therefore $\\var{easy1}\\times\\var{easy2}=\\var{easyans}$.
\n\nThis procedure works because it is the following in disguise:
\n$\\begin{align}\\var{easy1}\\times\\var{easy2}&=\\frac{\\var{easydig1}}{\\var{easyfact1}}\\times\\frac{\\var{easydig2}}{\\var{easyfact2}}&&\\text{(convert the decimals to fractions)}\\\\&=\\frac{\\var{easydig1}\\times\\var{easydig2}}{\\var{easyfact1}\\times\\var{easyfact2}}&&\\text{(multiply the fractions)}\\\\&=\\frac{\\var{easydigprod}}{\\var{easyfactprod}}\\\\&=\\var{easyans}&&\\text{(convert back to a decimal)}\\end{align}$
\n______________________________________________________________________________________
\nb) Remove the decimal points, do the multiplication of whole numbers, then put the decimal place in the answer so that the number of decimal places in the question and the answer are the same.
\nThis procedure works because it is the following in disguise:
\n$\\begin{align}\\var{adec1}\\times\\var{adec2}&=\\frac{\\var{atopnum}}{\\var{afact1}}\\times\\frac{\\var{abotnum}}{\\var{afact2}}&&\\text{(convert the decimals to fractions)}\\\\&=\\frac{\\var{atopnum}\\times\\var{abotnum}}{\\var{afact1}\\times\\var{afact2}}&&\\text{(multiply the fractions)}\\\\&=\\frac{\\var{aans}}{\\var{afactprod}}\\\\&=\\var{adecans}&&\\text{(convert back to a decimal)}\\end{align}$
\n\n
That is,
\nand therefore $\\var{adec1}\\times\\var{adec2}=\\var{adecans}0$. But note, we don't need to write the last zero so we could also write $\\var{adec1}\\times\\var{adec2}=\\var{adecans}$.
\nand therefore $\\var{adec1}\\times\\var{adec2}=\\var{adecans}00$. But note, we don't need to write the two trailing zeros so we could also write $\\var{adec1}\\times\\var{adec2}=\\var{adecans}$.
\nand therefore $\\var{adec1}\\times\\var{adec2}=\\var{adecans}$.
\n__________________________________________________________________________________________________
\nHow to calculate $\\var{atopnum}\\times\\var{abotnum}$
\nGenerally we set up $\\var{atopnum}\\times\\var{abotnum}$ with the ones and tens columns lined up vertically:
\n| \n | $\\var{atop[1]}$ | \n$\\var{atop[0]}$ | \n$\\times$ | \n
| \n | $\\var{abot[1]}$ | \n$\\var{abot[0]}$ | \n\n |
| \n | $\\phantom{0}$ | \n\n | \n |
We need to multiply each digit in the bottom number by each digit in the top number whilst respecting their place values.
\n\nWe multiply the digits in the ones column, that is, $\\color{green}{\\var{abot[0]}\\times \\var{atop[0]}}$.
\nSince this is just $\\var{ab0t0}$ we write $\\var{ab0t0}$ under the line in the ones column.
\nSince this is $\\var{ab0t0}$ we write the $\\var{ab0t0last}$ under the line in the ones column and carry the $\\var{ab0t0carry}$ into the tens column to be dealt with in the next step.
\n\n| \n | $\\overset{\\color{red}{\\var{ab0t0carry}}}{\\var{atop[1]}}$ $\\overset{\\phantom{1}}{\\var{atop[1]}}$ | \n$\\color{green}{\\overset{\\phantom{1}}{\\var{atop[0]}}}$ | \n$\\times$ | \n
| \n | $\\var{abot[1]}$ | \n$\\color{green}{\\var{abot[0]}}$ | \n\n |
| \n | \n | $\\color{red}{\\var{ab0t0last}}$ | \n\n |
We now multiply diagonally, $\\color{green}{\\var{abot[0]}\\times \\var{atop[1]}}$.
\nThis just gives us $\\var{ab0t1}$ so we write $\\var{ab0t1}$ under the line in the tens column.
\nThis gives us $\\var{ab0t1}$ so we write this under the line with the $\\var{ab0t1last}$ in the tens column.
\nThis gives us $\\var{ab0t1}$ but we have to add the $\\var{ab0t0carry}$ we carried earlier and so we write $\\var{ab0t1pluscarry}$ under the line with the $\\var{ab0t1last}$ in the tens column.
\nThis gives us $\\var{ab0t1}$ but we have to add the $\\var{ab0t0carry}$ we carried earlier and so we write $\\var{ab0t1pluscarry}$ under the line in the tens column.
\n\n| \n | $\\color{green}{\\overset{{\\var{ab0t0carry}}}{\\var{atop[1]}}}$ $\\color{green}{\\overset{\\phantom{1}}{\\var{atop[1]}}}$ | \n$\\overset{\\phantom{1}}{\\var{atop[0]}}$ | \n$\\times$ | \n
| \n | $\\var{abot[1]}$ | \n$\\color{green}{\\var{abot[0]}}$ | \n\n |
| $\\color{red}{\\var{ab0t1carry}}$ | \n$\\color{red}{\\var{ab0t1last}}$ | \n${\\var{ab0t0last}}$ | \n\n |
We are now finished with the digit $\\var{abot[0]}$ and move on to work with the $\\var{abot[1]}$ in the tens column. Since this is really a $\\var{abot[1]*10}$ we place a zero in the ones column on the next line to pad our numbers out. We also crossout or erase any carry marks that we have used.
\n\n| \n | $\\overset{\\phantom{1}}{\\var{atop[1]}}$ | \n$\\overset{\\phantom{1}}{\\var{atop[0]}}$ | \n$\\times$ | \n
| \n | $\\var{abot[1]}$ | \n$\\var{abot[0]}$ | \n\n |
| ${\\var{ab0t1carry}}$ | \n${\\var{ab0t1last}}$ | \n${\\var{ab0t0last}}$ | \n\n |
| \n | \n | $\\color{red}0$ | \n\n |
We now multiply along the other diagonal, that is, $\\color{green}{\\var{abot[1]}\\times\\var{atop[0]}}$.
\nSince this is just $\\var{ab1t0}$ we write $\\var{ab1t0}$ under the line in the tens column.
\nSince this is $\\var{ab1t0}$ we write the $\\var{ab1t0last}$ under the line in the tens column and carry the $\\var{ab1t0carry}$ into the tens column to be dealt with in the next step.
\n\n| \n | $\\overset{\\color{red}{\\var{ab1t0carry}}}{\\var{atop[1]}}$ $\\overset{\\phantom{1}}{\\var{atop[1]}}$ | \n$\\color{green}{\\overset{\\phantom{1}}{\\var{atop[0]}}}$ | \n$\\times$ | \n
| \n | $\\color{green}{\\var{abot[1]}}$ | \n$\\var{abot[0]}$ | \n\n |
| ${\\var{ab0t1carry}}$ | \n${\\var{ab0t1last}}$ | \n${\\var{ab0t0last}}$ | \n\n |
| \n | $\\color{red}{\\var{ab1t0last}}$ | \n${0}$ | \n\n |
We now multiply the digits in the tens column, that is, $\\color{green}{\\var{abot[1]}\\times \\var{atop[1]}}$.
\nThis just gives us $\\var{ab1t1}$ so we write $\\var{ab1t1}$ under the line in the hundreds column.
\nThis gives us $\\var{ab1t1}$ so we write this under the line with the $\\var{ab1t1last}$ in the hundreds column.
\nThis gives us $\\var{ab1t1}$ but we have to add the $\\var{ab1t0carry}$ we carried earlier and so we write $\\var{ab1t1pluscarry}$ under the line with the $\\var{ab1t1last}$ in the hundreds column.
\nThis gives us $\\var{ab1t1}$ but we have to add the $\\var{ab1t0carry}$ we carried earlier and so we write $\\var{ab1t1pluscarry}$ under the line in the hundreds column.
\n\n| \n | \n | $\\color{green}{\\overset{{\\var{ab1t0carry}}}{\\var{atop[1]}}}$ $\\color{green}{\\overset{\\phantom{1}}{\\var{atop[1]}}}$ | \n$\\overset{\\phantom{1}}{\\var{atop[0]}}$ | \n$\\times$ | \n
| \n | \n | $\\color{green}{\\var{abot[1]}}$ | \n$\\var{abot[0]}$ | \n\n |
| \n | ${\\var{ab0t1carry}}$ | \n${\\var{ab0t1last}}$ | \n${\\var{ab0t0last}}$ | \n\n |
| $\\color{red}{\\var{ab1t1carry}}$ | \n$\\color{red}{\\var{ab1t1last}}$ | \n${\\var{ab1t0last}}$ | \n${0}$ | \n\n |
We now add the two results to get the total, that is, $\\color{green}{\\var{asum1}+\\var{asum2}}$.
\n\n| \n | \n | $\\overset{{\\var{ab1t0carry}}}{\\var{atop[1]}}$ $\\overset{\\phantom{1}}{\\var{atop[1]}}$ | \n$\\overset{\\phantom{1}}{\\var{atop[0]}}$ | \n$\\times$ | \n
| \n | \n | $\\var{abot[1]}$ | \n$\\var{abot[0]}$ | \n\n |
| \n | $\\color{green}{\\var{ab0t1carry}}$ | \n$\\color{green}{\\var{ab0t1last}}$ | \n$\\color{green}{\\var{ab0t0last}}$ | \n$+$ | \n
| $\\color{green}{\\var{ab1t1carry}}$ | \n$\\color{green}{\\var{ab1t1last}}$ | \n$\\color{green}{\\var{ab1t0last}}$ | \n$\\color{green}{0}$ | \n\n |
| $\\color{red}{\\var{aanstho}}$ | \n$\\color{red}{\\var{aanshun}}$ | \n$\\color{red}{\\var{aansten}}$ | \n$\\color{red}{\\var{aansone}}$ | \n\n |
$\\var{atopnum}\\times\\var{abotnum}$ is therefore $\\var{aans}$.
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\nUse the long multiplication method.
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", "licence": "None specified"}, "statement": "\n\nThe proportion of students at {school} school who have been identified as being gifted is {dec1}.
\nHowever, only {dec2} of those students receive additional support in the classroom.
", "advice": "\n{dec2} of the students identified as being gifted at {school} school receive additional support in the classroom.
\nTherefore, 1 - {dec2} = {1-dec2} of the students that are gifted do NOT receive additional support in the classroom.
\nSo, {1-dec2} of the students that are gifted do NOT receive additional support in the classroom, and the students identified as being gifted are {dec1} of the whole school population.
\nWe need to find {1-dec2} of {dec1}.
\nTo find a proportion of a proportion, we multiply.
\nWe need to evaluate {1-dec2} x {dec1}.
\nTo multiply decimals without a calculator, you could convert each decimal to a fraction, then multiply, then convert back to a decimal:
\n{1-dec2} x {dec1} = $\\frac {\\var{10-num2}} {10} \\times \\frac {\\var{num1}} {10} = \\frac {\\var{(10-num2)*num1}} {100}$ = {(10-num2)*num1/100}
\nAlternatively, multiply the numbers (ignoring decimal points), then count the total number of decimal places in the question. Put the decimal point back in, ensuring that the answer has this same number of decimal places.
\n{10-num2} x {num1} = {num1*(10-num2)}. There are two digits after the decimal point in the question (two decimal places in the question), so the answer requires two digits after the decimal point.
\n{1-dec2} x {dec1} = {(1-dec2)*dec1}
\nThe proportion of all students at {school} school who have been identified as being gifted, but do not receive additional support in the classroom is {(1-dec2)*dec1}.
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", "templateType": "anything", "can_override": false}, "num1": {"name": "num1", "group": "Ungrouped variables", "definition": "dec1*10", "description": "The numerator for dec1.
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", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["school", "dec1", "dec2", "num1", "num2"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"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, "prompt": "What proportion of all students in the school have been identified as being gifted, but do not receive additional support in the classroom?
\nEvaluate without using a calculator.
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", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "Evaluate the following without using a calculator.
\n", "advice": "a) Convert the division/fraction into an equivalent division/fraction where we are dividing by a whole number. Do this by multiplying both $\\var{p}$ and ${1.2}$ by $10$ so that the decimal points are moved one place to the right.
\nNote we want the divisor to be a whole number but we don't need the dividend (1.2) to be whole.
\nb) Convert the division/fraction into an equivalent division/fraction where we are dividing by a whole number. Do this by multiplying both $\\var{s}$ and ${0.03}$ by $100$ so that the decimal points are moved two places to the right.
\nc) We are dividing by a whole number already so divide $\\var{t}$ by 6.
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$\\var{p}\\div{1.2}=$[[0]]
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\nUse a pen and paper to track your working.
\nDo not use a calculator.
\nTo check whether your answer is correct, click on Submit answer.
\nTo see a worked solution, click on Reveal answers.
\nTo try another version of the question, click on Try another question like this one.
\nTo try a different question, click on Go back to the menu (at top left hand side of screen).
\nTo exit the exercise, close the page.
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