91Ó°ÊÓ

Uncertainty represents the range of values that can be logically attributed to a determined quantity by comparing the parameter with the outcome of a measurement.

The equation for percent uncertainty in the distance is:

$\%\mathrm{Uncertainty}=\frac{\left(\mathrm{Uncertainty}\mathrm{in}\mathrm{distance}\right)}{\left(\mathrm{Original}\mathrm{value}\right)}×100$

Given data:

Uncertainty in the distance,$a=Â\pm 2\mathrm{m}$

Distance of the satellite,$d=20000\mathrm{km}$

Percent uncertainty in the distance can be calculated as:

$\begin{array}{c}\%\mathrm{Uncertainty}=\left(\frac{a}{d}\right)×100\\ \%\mathrm{Uncertainty}=\frac{\left(Â\pm 2\mathrm{m}×\frac{{10}^{-3}\mathrm{km}}{1\mathrm{km}}\right)}{\left(20000\mathrm{km}\right)}×\left(100\right)\\ \%\mathrm{Uncertainty}=1×{10}^{-5}\%\end{array}$

Thus, uncertainty in the distance is $1×{10}^{-5}\%$.

Convert the distance into meters as:

$\begin{array}{l}d=\left(20000\mathrm{km}\right)\left(\frac{{10}^3\mathrm{m}}{1\mathrm{km}}\right)\\ d=20000000\mathrm{m}\end{array}$

The distance between the satellite and the Earth with uncertainty is:

$d=20000000\mathrm{m}Â\pm 2\mathrm{m}$

Thus, eight significant figures are needed in the measurement of distance.

$d=20000000\mathrm{m}Â\pm 2\mathrm{m}$