### Video Transcript

A distance of 115 meters is
measured to the nearest meter. The distance is run in a time
of 12 seconds, measured to the nearest second. Rounding to an appropriate
number of significant figures, what was the average running speed?

We have here a situation where
a runner travels a distance, we’ll call it 𝑑, of 115 meters in a time, we’ll
call it 𝑡, of 12 seconds. The runner’s average speed 𝑣
is given by the distance traveled divided by the time taken to travel that
distance. When we calculate the speed,
though, we need to be careful to take into account the difference in significant
figures in our distance and time. The distance of 115 meters has
one, two, three significant figures. We know this because we’re told
the distance is measured to the nearest meter, meaning that each whole meter is
significant. Similarly, the time is measured
to the nearest second, which means that this time of 12 seconds has one, two
significant figures.

Whenever we combine values that
have different numbers of significant figures like these two do here, our final
answer keeps only the smallest number of significant figures of any of the
values involved. In this case, that smallest
number is two, the number of significant figures in our time 𝑡. When we calculate this
fraction, the exact answer we get is 9.583 repeating meters per second. But we recall that we’ll only
keep one, two significant figures in this final answer. All nonzero digits are
significant. So that means this is a
significant figure, and so is this. To round to two significant
figures then, we’ll look at this digit, which we see is greater than or equal to
five. And that means we will round
up. To two significant figures, the
runner’s average speed is 9.6 meters per second.