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 \(d = 1.49 \times {10^{11}}\;{\rm{m}}\) and \(d = 1.49 \times {10^8}\;{\rm{km}}\).

Step-by-step solution

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, \(d = 93\;{\rm{million - miles}}\)

(a)

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

\(\begin{aligned}{l}d = \left( {93\;{\rm{million - miles}} \times \frac{{{{10}^6}\;{\rm{miles}}}}{{1\;{\rm{million - miles}}}}} \right)\\ = \left( {93 \times {{10}^6}\;{\rm{miles}} \times \frac{{1609.34\;{\rm{meters}}}}{{1\;{\rm{mile}}}}} \right)\\ = 1.49 \times {10^{11}}\;{\rm{m}}{\rm{.}}\end{aligned}\)

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

\(\begin{aligned}{l}d = \left( {1.49 \times {{10}^{11}}\;{\rm{m}} \times \frac{{1\;{\rm{km}}}}{{1000\;{\rm{m}}}}} \right)\\ = 1.49 \times {10^8}\;{\rm{km}}{\rm{.}}\end{aligned}\)

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