Brilliant Bounds!

In a previous post I wrote about fractions that appear on roadsigns. 

I had gone with an initial assumption that quarters and halves were the fractions that appear on UK road-signs, but then we saw one that featured one-third!   

My new assumption is that these fractions appear on UK road signs:

 

This is brilliant if we want to think about upper/lower bounds.

Assuming that the bounds are halfway between one measurement and the next, this gives:

If we put them all over 24 then the upper/lower bounds are:

 

There is something rather pleasing about these!

Least accurate measurement?

According to the Department for Transport: “A sign may indicate the distance to a destination in miles. Fractions of a mile may be shown for distances less than 3 miles.”  This means that distances less than 3 miles can be given rather accurately because they can use the fractions shown above. 

A final question: which exact measurement (whether greater or smaller than 3 miles) has the largest percentage error?