Question

Use scientific notation to express a light year in miles.

Answer 1

Hint: A light year is defined as the distance travelled by a light ray in one complete year. So, we have to calculate the distance travelled by a light ray in one complete year in miles in order to convert a light year in miles. Distance travelled by a light ray is calculated by using the formula \[Distance = \left( {Time} \right)\left( {Speed} \right)\].

Complete step-by-step answer:
We know that the speed of light is $ \left( {3 \times {{10}^8}} \right)m{s^{ - 1}} $ .
Number of days in one complete year $ = 365 $
Number of hours in a single day $ = 24 $
So, Number of hours in one complete year = $ 365 \times 24 $
Number of minutes in one hour $ = 60\min $
Number of minutes in one complete year $ = 365 \times 24 \times 60\min $
Number of seconds in one minute $ = 60\sec $
Number of seconds in one complete year $ = $ $ 365 \times 24 \times 60 \times 60\sec $
 $ = 365 \times 24 \times 3600\sec $
 $ = 8760 \times 3600\sec $
On solving further,
 $ = $ $ 31,536,000\sec $
Now, distance travelled by light ray in one year $ = $ (Time) $ \times $ (Speed of light)
 $ = $ $ 31,536,000 \times 3 \times {10^8}meters $
 $ = $ $ 94,608 \times {10^{11}}\;meters $
Now we have to convert metres into miles. Hence, the conversion $ 1metre = 0.0006214\;miles $ will help us to convert metres into miles. So, converting metres into miles, we get,
 $ = $ $ 94,608 \times {10^{11}} \times 0.0006214\;miles $
 $ = $ $ 58.7894112 \times {10^{11}}\;miles $
 $ = $ $ 5.87894112 \times {10^{12}}\;miles $
Hence, Light years in miles can be written as $ 5.87894112 \times {10^{12}}\;miles $ .
So, the correct answer is “ $ 5.87894112 \times {10^{12}}miles $ ”.

Note: The given problem can also be solved by first converting the speed of light from $ m{s^{ - 1}} $ to $ miles{\left( {second} \right)^{ - 1}} $ and then multiplying it with the time duration in seconds so as to get the distance travelled by light in one complete year in miles. Care should be taken while converting units of distance from metres to miles and while carrying out subsequent calculations