OpenStax College Physics, Chapter 1, Problem 8 (Problems & Exercises)

This is College Physics Answers with Shaun Dychko. The speed of sound is measured to be 342 meters per second; we are going to convert this into kilometers per hour and so we need to think of what conversion factor's we can use that will cancel away the units we don't want leaving us with units that we do want. So considering the meters, we want to turn the meters into kilometers and so we multiply by 1 kilometer for every 1000 meters and then meters has to be on the denominator of this conversion factor in order to cancel the meters in the numerator of the speed that we are given. So the next conversion factor is going to cancel away the seconds that are in the denominator of the measurement we are given and so we write seconds on the top and I have, you know, you may not have it memorized that there are 3600 seconds in an hour so we can do our conversion to hours in two steps say. So we have 60 seconds in a minute and so these seconds cancel which is good and we are left with minutes though which is not finished because we want to have hours. And so we multiply by 60 minutes for every hour and this leaves us with units, kilometers per hour. And the arithmetic that one has to do is divide 342 by a 1000 then multiply by 60 and then multiply by 60 again and you get 1230 kilometers per hour. This has three significant figures when you write it this way although it's a little bit ambiguous because it's not entirely clear whether the zero is significant or not; technically, it is not but one could make a mistake and think that it is. So to be absolutely precise, you could say 1.23 times 10 to the 3 kilometers per hour; this is scientific notation here.