Evaluating method & dimensional analysis

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A quantity you deliberately keep **constant** during an experiment so it can't affect the result and the test stays fair.

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A reading clearly **out of line** with the others (a one-off mistake) — discard it before averaging.

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To reduce **random** uncertainty — the chance scatter up and down partly **cancels**, so the mean is more reliable.

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**No** — a systematic error shifts every reading the same way. Fix the instrument or method (e.g. zero it).

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Random = readings **scatter** around the true value (cured by averaging). Systematic = all readings **shifted** one way (not cured by averaging).

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Balancing the **fundamental SI units** (kg, m, s, A) on both sides of an equation — to find an unknown power or state a constant's units.

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Divide the **y-axis units by the x-axis units** (gradient = rise ÷ run), then simplify.

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Balance the **base units one at a time** — each base unit (kg, m, s) gives one equation for the powers.

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**kg m s⁻²** (the newton, N = kg m s⁻²).

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**kg m² s⁻²** (the joule, J = N m = kg m² s⁻²).

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Add the **fractional** uncertainties: $\dfrac{\Delta y}{y} = \dfrac{\Delta a}{a} + \dfrac{\Delta b}{b} + \dfrac{\Delta c}{c}$.

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Add the **absolute** uncertainties: $\Delta y = \Delta a + \Delta b$ (it's a derived rule, not always printed).

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Multiply the fractional uncertainty by $|n|$: $\dfrac{\Delta y}{y} = |n|\,\dfrac{\Delta a}{a}$.