I have a vertex on a 45 degree edge. I want to slide that vertex exactly $0.1m$ on the $x$-axis, but maintain a $y$ and $z$ position along the edge. I can slide the vertex along the edge using GG for vertex slide, but I do not know the percentage of the length of the edge that corresponds to $0.1m$. How can I do this?
Set Transformation Orientation to View. In Edit Mode, select your Edge and press Shift+NumPad7 to align to your viewport. Now you can manipulate the vertex location by using the View's Y perspective. Select the vertex and press GY-0.1mEnter
You can also use Shift+NumPad3 to view from the side and use the View's X perspective then press GX-0.1mEnter but it's not so visually appealing for this example.
Try pressing the x axis to slide on that axis, then press 0.1 on your keyboard. Your units I think should also be in the same unit (in this case meters) that you want to vertex slide in. You could also do -0.1 or when you vertex slide, a pop up should appear on your bottom left corner of your screen. You can type 0.1 in the slot to make the vertex the way you want.