Approximately Irrational Road Repair?

There is some road work being done right near our house. I think it's just some simple repaving. As one drives up to the place where the roadwork will start, there is one of those rectangular signs alerting motorists that there will be road construction for a little while. In particular, the sign says:

Roadwork next 1.41 Miles

This raises a number of questions. First, how many digits are really needed? Would alerting drivers that the construction will last for 1.4 miles be sufficient? How can the additional one hundredth of a mile matter?

But maybe the 1.41 arose because they were trying to approximate the square root of two. Maybe the construction follows the hypotenuse of an isosceles triangle whose legs have a length of one mile. The stretch of road is sufficiently curvey that this doesn't seem to be a possibility. Nevertheless, it's a fun thing to think about.