calculate the following: (48.98 ± 4.11) km/h + (15.24 ± 4.44) km/h. round based on the applicable rules of…

Explanation:

Step1: Add the values without uncertainties

$48.98 + 15.24=64.22$

Step2: Add the uncertainties

$4.11 + 4.44 = 8.55$

Step3: Round the sum and uncertainty

Rounding $64.22$ to two decimal - places gives $64.22$ (since there are no specific rounding - off rules other than general decimal - place rules mentioned). Rounding $8.55$ to two decimal - places gives $8.55$.

Answer:

$(64.22\pm8.55)$ km/h

Explanation for Question 7:

Step1: Calculate the nominal value of the current

$I=\frac{V}{R}=\frac{220}{830}\approx0.265$ A

Step2: Calculate the relative uncertainty in current

The relative uncertainty in a quotient $\frac{V}{R}$ is given by $\frac{\Delta I}{I}=\sqrt{(\frac{\Delta V}{V})^2+(\frac{\Delta R}{R})^2}$. $\frac{\Delta V}{V}=2.2% = 0.022$ and $\frac{\Delta R}{R}=1.3%=0.013$. $\frac{\Delta I}{I}=\sqrt{(0.022)^2+(0.013)^2}=\sqrt{0.000484 + 0.000169}=\sqrt{0.000653}\approx0.0256$ or $2.56%$

Step3: Calculate the uncertainty in current

$\Delta I = I\times\frac{\Delta I}{I}=0.265\times0.0256\approx0.0068$ A

Answer:

$I = 0.265\pm0.007$ A (rounded to three decimal - places for the value of current and three significant figures for the uncertainty) and $2.6%$ (rounded to one decimal - place for the relative uncertainty)