# Uncertainty

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In general, uncertainty of a reading is determined to the nearest half of the smallest graduation.

• Always quoted to one significant figure.

Numerical value of uncertainty is the absolute uncertainty or actual uncertainty.

Uncertainty of an instrument determined the number of decimal places that should be quoted for the readings taken from it. The number of decimal places I a reading is the same as that in the uncertainty.

A lower percentage uncertainty will mean the instrument used to measure it is more acceptable.

Fractional Uncertainty = $\frac{\Delta R}{R}$

Percentage Uncertainty = $\frac{\Delta R}{R} \times 100 \%$

If $Y = a + b$ OR $Y = a – b$, uncertainty of Y is $\Delta Y = \Delta a + \Delta b$

Because we are always maximizing the possible uncertainty that can occur.

Important: Make X the subject to find the uncertainty of X.

If $Y = a \times b$ OR $Y = \frac{a}{b}$, uncertainty of Y is $\frac{\Delta Y}{Y} = \frac{\Delta a}{a} + \frac{\Delta b}{b}$

If $Y = a^{n} \: = \: a \: \times \: a \: \times \: a \: \times \: a \:….$, then uncertainty of Y is $\frac{\Delta Y}{Y} = n \frac{\Delta a}{a}$