Question

The sun, on average, is 93 million miles from the earth. How many meters is this? Express (a) using powers of 10, and (b) using a metric prefix (km).

Short answer

The results obtained for parts (a) and (b) are $d=1.49\times {10}^{11}\mathrm{m}$and $d=1.49\times {10}^8\mathrm{km}$.

Step-by-step solution

Step 1. Converting miles into meters

Mile is a unit of measurement of distance. One mile is equivalent to 5280 feet.

Given data:

Distance of the sun from the earth,$d=93\mathrm{million}-\mathrm{miles}$

(a)

Using the formula to express a million miles in meters, you get

$\begin{array}{c}d=\left(93\mathrm{million}-\mathrm{miles}\times \frac{{10}^6\mathrm{miles}}{1\mathrm{million}-\mathrm{miles}}\right)\\ =\left(93\times {10}^6\mathrm{miles}\times \frac{1609.34\mathrm{meters}}{1\mathrm{mile}}\right)\\ =1.49\times {10}^{11}\mathrm{m}.\end{array}$

Step 2. Converting meters into kilometers

For converting meters into kilometers, divide the given distance by a factor of 1000.

(b)

Using the formula to determine the distance with the metric prefix, you get

$\begin{array}{c}d=\left(1.49\times {10}^{11}\mathrm{m}\times \frac{1\mathrm{km}}{1000\mathrm{m}}\right)\\ =1.49\times {10}^8\mathrm{km}.\end{array}$

Thus, the values of distance in powers of 10 and in the metric prefix are $1.49\times {10}^{11}\mathrm{m}$and $1.49\times {10}^8\mathrm{km}$, respectively.