The distance travelled by a beam of light can be written as;
[tex]\text{Distance = Speed }\times\text{ time}[/tex]The speed of a beam of light is given as;
[tex]\text{Speed = 186,000 miles/second}[/tex]The time given should be converted to seconds.
[tex]\begin{gathered} Time=4years\text{ } \\ there\text{ are }31536000\text{ seconds in a year.} \\ \text{Time = 4 years }\times31536000\text{ seconds/year} \\ Time\text{ = 126,144,000 seconds.} \end{gathered}[/tex]So, applying the formula for distance and substituting the given values, we have;
[tex]\begin{gathered} \text{Distance = Speed}\times Time \\ \text{Distance = 186,000 miles/second }\times\text{ 126,144,000 seconds.} \\ \text{Distance = 23,462,784,000,000 miles} \end{gathered}[/tex]Then expressing it in scientific notation we have;
[tex]\begin{gathered} \text{ Distance = 23,462,784,000,000 miles} \\ \text{ Distance = 2.35 }\times10^{13}\text{ miles} \end{gathered}[/tex]Therefore, the distance a beam of light will travel in four years is;
[tex]\text{ Distance = 2.35 }\times10^{13}\text{ miles}[/tex]