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\textbf{Practice Problem - Approach and Solutions}  \begin{enumerate}  \item{Errors are differences between the measured value and the real value of a property due to systematic (miscalibration/bias) issues or random (gaussian) fluctuations. Uncertainties come from lack of resolution in the scale of the equipment being used, or our own ability to measure. Don't discuss human errors, as it's too general to be useful, and if you're following the correct experimental procedure then other (more important!) sources of uncertainty should dominate.}  \item{Add values, add uncertainties: \item{  Under the assumption that the errors are normally distributed, we can do better than straight addition:  \begin{align*}  \text{Sum} &= \sum_{i=1}^N{x_i} \pm \sum_{i=1}^N{\delta x_i}\\ \sqrt{\sum_{i=1}^N{\delta x_i^2}}\\  &= (102.3+44.8+5.67) \pm (0.2+0.2+0.08)\\ \sqrt{0.2^2+0.2^2+0.08^2}\\  &= 152.77 \pm 0.48\\ 0.29\\  &= 152.8 \pm 0.5 0.3  \text{cm} \end{align*}  #Add values, add uncertainties:  #\begin{align*}  #\text{Sum} &= \sum_{i=1}^N{x_i} \pm \sum_{i=1}^N{\delta x_i}\\  #&= (102.3+44.8+5.67) \pm (0.2+0.2+0.08)\\  #&= 152.77 \pm 0.48\\  #&= 152.8 \pm 0.5 \text{cm}  #\end{align*}  }  \item{Multiply values to find distance, add relative uncertainties, multiply relative uncertainty by distance to get absolute uncertainty.  \begin{align*}