AQA · A-Level · Physics
Course version: 7408 · Version from Sept 2016
Combination of absolute and percentage uncertainties.
Full specification wording
Limitation of physical measurements: Combination of absolute and percentage uncertainties.
When a quantity is calculated from several measurements, their uncertainties must be combined.
Checked against the AQA 7408 specification (opens in a new tab) on .
- Point 4 of 7
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
When a quantity is calculated from several measurements, their uncertainties must be combined. For addition and subtraction, add the absolute uncertainties. If a rod is made of two lengths, 0.842 m ± 0.001 m and 0.315 m ± 0.001 m, the total is 1.157 m ± 0.002 m. For multiplication and division, add the percentage uncertainties instead. If a rectangle has length 0.842 m ± 0.119% and width 0.315 m ± 0.317%, the area has a percentage uncertainty of about 0.436%. Raising a quantity to a power multiplies its percentage uncertainty by that power. Choose the rule that matches the arithmetic, convert between forms as needed, and state the final absolute uncertainty to one significant figure.
What earns the marks
- For addition and subtraction, combine the absolute uncertainties by adding them, keeping the unit of the quantity.
- For multiplication and division, combine the percentage uncertainties by adding them.
- For a quantity raised to a power, multiply its percentage uncertainty by that power.
- Convert between absolute and percentage forms when the calculation mixes operations.
- State the final combined uncertainty to one or two significant figures, matching the decimal places of the calculated value.
Common mistakes and how to put them right
Adding percentage uncertainties when quantities are added or subtracted.
Put it right by adding absolute uncertainties for those operations.
Adding absolute uncertainties when quantities are multiplied or divided.
Put it right by converting to percentage uncertainties and adding those.
Giving the absolute uncertainty to too many significant figures.
Put it right by rounding the uncertainty to one (or two) significant figures and matching the value's decimal places.
Exam tips
- Identify the arithmetic first: addition and subtraction use absolute uncertainties, while multiplication, division and powers use percentage uncertainties.
- Round the final absolute uncertainty to one significant figure and ensure the calculated value is given to the same number of decimal places.
Try the lesson
The start of the Limitation of physical measurements: Combination of absolute and percentage uncertainties. lesson, made from checked teaching notes for this specification point.
Have a go first
Two lengths are added together: 12 cm ± 1 cm and 8 cm ± 1 cm. What is the absolute uncertainty in the total length?
Listen
When a quantity is calculated from several measurements, their uncertainties must be combined. For addition and subtraction, add the absolute uncertainties. If a rod is made of two lengths, 0.842 m ± 0.001 m and 0.315 m ± 0.001 m, the total is 1.157 m ± 0.002 m. For multiplication and division, add the percentage uncertainties instead. If a rectangle has length 0.842 m ± 0.119% and width 0.315 m ± 0.317%, the area has a percentage uncertainty of about 0.436%. Raising a quantity to a power multiplies its percentage uncertainty by that power. Choose the rule that matches the arithmetic, convert between forms as needed, and state the final absolute uncertainty to one significant figure. A strong answer earns marks for these points. For addition and subtraction, combine the absolute uncertainties by adding them, keeping the unit of the quantity. For multiplication and division, combine the percentage uncertainties by adding them. For a quantity raised to a power, multiply its percentage uncertainty by that power. Convert between absolute and percentage forms when the calculation mixes operations. A common slip: Adding percentage uncertainties when quantities are added or subtracted. Instead, adding absolute uncertainties for those operations. Exam tip: Identify the arithmetic first: addition and subtraction use absolute uncertainties, while multiplication, division and powers use percentage uncertainties.
See it
Key words
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Combination of absolute and percentage uncertainties
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Addition and subtraction rule
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Multiplication and division rule
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Raising to a power
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See every definition
- Combination of absolute and percentage uncertainties
- When a quantity is calculated from several measurements, their uncertainties must be combined using the rule that matches the arithmetic.
- Addition and subtraction rule
- For addition and subtraction, combine the absolute uncertainties by adding them, keeping the unit of the quantity.
- Multiplication and division rule
- For multiplication and division, combine the percentage uncertainties by adding them instead of the absolute uncertainties.
- Raising to a power
- Raising a quantity to a power multiplies its percentage uncertainty by that power.
Label the diagram
Some boxes have lost their names. Pick the right name for each number.
1Box 1
2Box 2
3Box 3
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