significant figures

Suppose you have a digital clock in your car, and a digital odometer.

When you get on the Interstate your odometer reads 43 587 miles and your clock reads 1:53.

When you get off the Interstate your odometer reads 43 594 miles and your clock reads 1:59.

As best you can tell you traveled 7 miles in 6 minutes.

So you conclude that you were traveling at 1.166666 miles per minute.

Most of the digits in 1.166666 are irrelevant to the quantity you are measuring.

You don't know how close the 43 587 was to 43 588, or how close the 43 594 was to 43 595. Your actual distance might have been closer to 6 miles or to 8 miles than to 7 miles.

And you don't know how close 1:53 was to 1:54, or how close 1:59 was to 2:00. The time could have been closer to 5 minutes or to 7 minutes than to 6 minutes.

So your average speed might have been as little as 6 miles / 7 minutes, about .9 miles / minute. Or it could have been as great at 8 miles / 5 minutes, about 1.6 miles / minute.

With this wide range of possibilities, it becomes clear that all those 6's are completely insignificant for this calculation. Your information doesn't have the precision to give even a 3-significant-figure result like 1.16 miles / minute. It isn't even good enough to justify a 2-figure result of 1.1 or 1.2 miles / minute.

Really the best you can say is that the 7 mile distance and the 6 minute time were good to about 1 significant figure, so you were traveling around 1 mile / minute.

Now if you were using a trip timer accurate to within .1 mile, and a watch with a second hand, you could easily get a 2-significant-figure result, and could even get close to 3 figures.