# Question Video: Determining Uncertainty in a speed Measurement Given the Uncertainty in the Distance and Time Measurements Physics • 9th Grade

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?

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### 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.