A number is in scientific notation if it is written as a decimal multiplied by some power of 10, where the decimal has exactly one digit in front of the decimal place. For example:
\n\\[1.234\\times 10^6, \\quad \\text{and} \\quad 3.01\\times 10^{-3}\\]
\nare both in scientific notation.
\n\nRecall that multiplying by powers of 10 moves the decimal point, for example multiplying a number by $10^\\var{pow1}$ (which is the same as multiplying by $\\var{10^pow1}$) moves the decimal point $\\var{pow1}$ places to make the number bigger (the decimal point moves to the right). In particular:
\n\\[\\var{dec1}\\times 10^\\var{pow1}= \\var{q1}\\]
\nNote there is a decimal point after the last zero that we do not write simply because there is no reason to.
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", "sortAnswers": false, "extendBaseMarkingAlgorithm": true, "type": "gapfill", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst"}, {"scripts": {}, "unitTests": [], "marks": 0, "gaps": [{"scripts": {}, "unitTests": [], "marks": 1, "mustBeReducedPC": 0, "customMarkingAlgorithm": "", "variableReplacements": [], "notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "showFeedbackIcon": true, "correctAnswerStyle": "plain", "mustBeReduced": false, "correctAnswerFraction": false, "extendBaseMarkingAlgorithm": true, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "maxValue": "{q2}", "showCorrectAnswer": true, "minValue": "{q2}"}], "customMarkingAlgorithm": "", "variableReplacements": [], "steps": [{"scripts": {}, "unitTests": [], "marks": 0, "customMarkingAlgorithm": "", "variableReplacements": [], "prompt": "A number is in scientific notation if it is written as a decimal multiplied by some power of 10, where the decimal has exactly one digit in front of the decimal place. For example:
\n\\[1.234\\times 10^6, \\quad \\text{and} \\quad 3.01\\times 10^{-3}\\]
\nare both in scientific notation.
\n\nRecall that multiplying by powers of 10 moves the decimal point, for example multiplying a number by $10^\\var{pow2}$ (which is the same as multiplying by $\\var{10^pow2}$) moves the decimal point $\\var{pow2}$ places to make the number bigger (the decimal point moves to the right). In particular:
\n\\[\\var{dec2}\\times 10^\\var{pow2}= \\var{q2}\\]
\nNote there is a decimal point after the last zero that we do not write simply because there is no reason to.
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", "sortAnswers": false, "extendBaseMarkingAlgorithm": true, "type": "gapfill", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst"}], "tags": ["converting", "scientific notation", "standard form"], "rulesets": {}, "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.
\n\nWrite the following numbers in decimal notation.
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\n\nWrite the following numbers in decimal notation.
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", "sortAnswers": false, "steps": [{"scripts": {}, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "type": "information", "customMarkingAlgorithm": "", "unitTests": [], "marks": 0, "variableReplacements": [], "prompt": "A number is in scientific notation if it is written as a decimal multiplied by some power of 10, where the decimal has exactly one digit in front of the decimal place. For example:
\n\\[1.234\\times 10^6, \\quad \\text{and} \\quad 3.01\\times 10^{-3}\\]
\nare both in scientific notation.
\n\nMultiplying a number by $10^\\var{pow1}$ will move the decimal point $\\var{-pow1}$ places to make the number smaller (the decimal point moves to the left). This is because
\n\\[10^\\var{pow1}=\\frac{1}{10^\\var{-pow1}}=\\frac{1}{\\var{10^-pow1}}=\\var{10^pow1}\\]
\nand so multiplying by it must make the original number smaller. In particular,
\n\\[\\var{dec1}\\times 10^\\var{pow1}=\\var{q1}\\]
\nNote you should always put a zero in front of your decimal point.
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", "sortAnswers": false, "steps": [{"scripts": {}, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "type": "information", "customMarkingAlgorithm": "", "unitTests": [], "marks": 0, "variableReplacements": [], "prompt": "A number is in scientific notation if it is written as a decimal multiplied by some power of 10, where the decimal has exactly one digit in front of the decimal place. For example:
\n\\[1.234\\times 10^6, \\quad \\text{and} \\quad 3.01\\times 10^{-3}\\]
\nare both in scientific notation.
\n\nMultiplying a number by $10^\\var{pow2}$ will move the decimal point $\\var{-pow2}$ places to make the number smaller (the decimal point moves to the left). This is because
\n\\[10^\\var{pow2}=\\frac{1}{10^\\var{-pow2}}=\\frac{1}{\\var{10^-pow2}}=\\var{10^pow2}\\]
\nand so multiplying by it must make the original number smaller. In particular,
\n\\[\\var{dec2}\\times 10^\\var{pow2}=\\var{q2}\\]
\nNote you should always put a zero in front of your decimal point.
", "showCorrectAnswer": true, "extendBaseMarkingAlgorithm": true}], "extendBaseMarkingAlgorithm": true}], "type": "question"}, {"name": "Scientific notation: large numbers to scientific notation", "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": ["converting", "scientific notation", "standard form"], "ungrouped_variables": ["dec1", "pow1", "q1", "dec2", "pow2", "q2"], "advice": "", "parts": [{"scripts": {}, "type": "gapfill", "variableReplacementStrategy": "originalfirst", "stepsPenalty": "1", "steps": [{"scripts": {}, "type": "information", "unitTests": [], "showFeedbackIcon": true, "prompt": "A number is in scientific notation if it is written as a decimal multiplied by some power of 10, where the decimal has exactly one digit in front of the decimal place. For example:
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\nare both in scientific notation.
\n\nSuppose we have the number $\\var{q1}$. In scientific notation, this number would start with $\\var{dec1}$ since we only want one digit in front of the decimal point. The decimal point is currently to the right of the last digit in $\\var{q1}$ and needs to move to between the first and second digits, that is $\\var{dec1}$. Count the places that the decimal point must jump and you get $\\var{pow1}$ places. That is,
\n\n\\[\\var{q1}=\\var{dec1}\\times 10^{\\var{pow1}}\\]
\n\nWe have a positive $\\var{pow1}$ as the power because we need to make the number $\\var{dec1}$ bigger to get to $\\var{q1}$.
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\n\nSuppose we have the number $\\var{q2}$. In scientific notation, this number would start with $\\var{dec2}$ since we only want one digit in front of the decimal point. The decimal point is currently to the right of the last digit in $\\var{q2}$ and needs to move to between the first and second digits, that is $\\var{dec2}$. Count the places that the decimal point must jump and you get $\\var{pow2}$ places. That is,
\n\n\\[\\var{q2}=\\var{dec2}\\times 10^{\\var{pow2}}\\]
\n\nWe have a positive $\\var{pow2}$ as the power because we need to make the number $\\var{dec2}$ bigger to get to $\\var{q2}$.
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\n\nWrite the following numbers in scientific notation.
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\nSuppose we have the number $\\var{q1}$. In scientific notation, this number would start with $\\var{dec1}$ since we only want one digit in front of the decimal point. The decimal point is currently here $\\var{q1}$ and needs to move to between the first and second digits, that is $\\var{dec1}$. Count the places that the decimal point must jump and you get $\\var{-pow1}$ places. That is,
\n\n\\[\\var{q1}=\\var{dec1}\\times 10^{\\var{pow1}}\\]
\n\nWe have a negative $\\var{-pow1}$ as the power because we need to make the number $\\var{dec1}$ smaller to get to $\\var{q1}$.
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\n\nWe have a negative $\\var{-pow2}$ as the power because we need to make the number $\\var{dec2}$ smaller to get to $\\var{q2}$.
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", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showFeedbackIcon": true, "customMarkingAlgorithm": ""}], "functions": {}, "rulesets": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "tags": ["converting", "scientific notation", "standard form"], "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.
\n\nWrite the following numbers in scientific notation.
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