The speed of light in a vacuum is 2.998×108 m/s . What is its speed in miles per minute (mi/min)?

Answer 1

Hi there! I am also a chemistry major so I can help you with this problem.

This problem deals with stoichiometry, which is a process to convert units of measurement and involves a lot of multiplication and division.

First, we need to know the number of meters that are in a mile. 1 Mile = ~1609 Meters. And we already know how many seconds are in 1 minute, 60.

Also, instead of writing "x 10^8", I'll write "E 8".

(2.998 E 8 m / 1 s) x (1 mile / 1609 m) x (60 s / 1 min) =

Do you see how the meters cancel (because we have it in the numerator and then it's in the denominator)? And then the seconds (first it's in the denominator and then the numerator)? Finally, you're left with miles/min.

Once you multiply everything in the numerator and divide by everything in the denominator (2.998 E 8 x 1 x 60 / 1 / 1609 / 1) you get 11179614.67, and in scientific notation (to be consistent with sigfigs), it would be 1.118 E 7.

I hope this helps! Please reach out if you have any further questions.