Question

The speed of light is about 300,000,000 m/s. The distance of Earth to Sol is about 148,490,000,000 meters. How long does it take the light from Sol to reach Earth ? Express your answer in seconds in scientific notation. Express your answer in hours in scientific notation. And express your answer in days in scientific notation.

Answer 1

To make things easier, we first write both quantities with scientific notation:

`\begin{gathered} \text{Speed of light:} \\ 300,000,000\text{ m/s }\rightarrow3\cdot10^8\text{ m/s} \\ 148490000000\text{ m }\rightarrow14849\cdot10^7\text{ m} \end{gathered}`

Now we can find how many seconds will it take the light to reach the sun with a simple division:

`(14849\cdot10^7)/(3\cdot10^8)=4.9496\cdot10^2\text{ }`

Therefore, it will take the light 4.9496x10^2 seconds to reach the sun.

Finally, to convert it to hours and days, we just have to divide by the corresponding equivalence:

`\begin{gathered} 1\text{ hour}\rightarrow3600\text{ seconds} \\ \Rightarrow(494.96)/(3600)=0.13748=13\cdot10^(-2) \\ 1\text{ day }\rightarrow86400\text{ seconds} \\ \Rightarrow(494.96)/(86400)=0.005728=57.28\cdot10^(-4) \end{gathered}`

Therefore, it will take the light 13.748x10^(-2) hours or 57.28x10^(-4) days to reach the sun.