Question

6. Traveling at approximately 186,000 miles per second, about how manymiles does a beam of light travel in four years? Express your answer inscientific notation.

Answer 1

The distance travelled by a beam of light can be written as;

`\text{Distance = Speed }*\text{ time}`

The speed of a beam of light is given as;

`\text{Speed = 186,000 miles/second}`

The time given should be converted to seconds.

`\begin{gathered} Time=4years\text{ } \\ there\text{ are }31536000\text{ seconds in a year.} \\ \text{Time = 4 years }*31536000\text{ seconds/year} \\ Time\text{ = 126,144,000 seconds.} \end{gathered}`

So, applying the formula for distance and substituting the given values, we have;

`\begin{gathered} \text{Distance = Speed}* Time \\ \text{Distance = 186,000 miles/second }*\text{ 126,144,000 seconds.} \\ \text{Distance = 23,462,784,000,000 miles} \end{gathered}`

Then expressing it in scientific notation we have;

`\begin{gathered} \text{ Distance = 23,462,784,000,000 miles} \\ \text{ Distance = 2.35 }*10^(13)\text{ miles} \end{gathered}`

Therefore, the distance a beam of light will travel in four years is;

`\text{ Distance = 2.35 }*10^(13)\text{ miles}`