Expanding on what Dave wrote:
SketchUp displays lengths according to the units you have set in the model info window. If your choice does not have enough precision to present a particular length perfectly, SketchUp displays the closest value allowed by your choice and prefixes it with "~" to let you know that the value shown is an approximation of the true value. It is important to realize this is an aspect of presenting values on the GUI, it does not mean the value isn't stored correctly inside SketchUp. Also, it is a one-way street: you can't enter a "~" prefix when you type a value.
For example, if you set units to decimal meters with 0.0 precision, the value 0.123m can't be fully displayed even if that is the exact length of the entity in the SketchUp model. It will be "~ 0.1m" even though SketchUp internally has the correct 0.123m value. Similarly, if you set fractional inches with 1/2 inch precision, 3/8 inch will display as "~ 1/2" because that's the closest value that can be displayed.