// Numbas version: exam_results_page_options {"name": "Decimals: Multiplying and dividing by powers of ten", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"statement": "

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

\n

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

", "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 $\\var{ans1}$.

\n

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

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

\n

", "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 $\\var{ans2}$.

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

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

\n

", "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 $\\var{ans3}$.

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

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

\n

", "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.

\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 $\\var{ans4}$.

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

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

", "extendBaseMarkingAlgorithm": true}], "extensions": [], "ungrouped_variables": ["dec1", "dec2", "dec3", "dec4", "power", "poweroften", "ans1", "ans2", "ans3", "ans4", "pronpower"], "rulesets": {}, "name": "Decimals: Multiplying and dividing by powers of ten", "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.

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.