You may subdivide the plane once. That way you would have 200 edgeloops along one side and 1 edgeloop on the opposite direction. Then you can Alt + Click the single edgeloop, hit X, choose Edge Loops.
Exactly 100 to 200 would be difficult since there’s odd number of edges after 100 cuts. But if you mean 201, i.e. insert cuts in between those other loops, then yeah, either @robi’s solution, or, select one edge loop that runs perpendicular to your original cuts, expand it to rings (Select -> Select Loops -> Edge Rings), and subdivide once.
I have a harder question. If I made a Torus with e.g. 48 loops around it, what is the way to reduce the number of those loops to 24, i.e. dissolve every other edge loop. Or 16 (dissolve every two out of three edge loops).
Pick Shortest Path and Select -> Checker Deselect are your friends
Select one edge ring along the torus (ring, not loop), Select -> Checker Deselect, Select -> Select Loops -> Edge Loops, dissolve edges.
With default keymap (and on a cylinder instead of torus) selecting the ring can be done by clicking one edge at the top, ctrl+clicking one at the bottom and in options checking both Face Stepping and Topology Distance; dissolution is, in edge mode, ctrl+x.
Options for both Checker Deselect and Pick Shortest Path can let you define a pattern other than every other edge.
Another way is to, in edge mode, select one edge in the ring, select one after next in the same ring (have to be done with click-selection to set active), do a bunch of Select -> Select More/Less -> Next Active, then convert to loops and dissolve.
I selected one Edge in one of the Loops. I went Select > Select Loops > Edge Rings. I went Checker Deselect on default settings. I went Select > Select Loops > Edge Loops. I went X, Dissolve Edges.
That it is. I kind of wish though that its variant bound to ctrl+click selected loops and rings on its own without fiddling with options, and didn’t even have options (or maybe had pre-defined options). That way it’d be even more useful as it wouldn’t clog up the Repeat function.
I found a good way to remove the edge loops in a pattern.
Select one edge in an edge ring. Shift select another edge in the ring skipping either 1,2,3, etc. edges. Use “Select More/Less > Next Active” repeatedly until you go around the ring. Then Select Edge Loops and X (Delete) > Edge Loops.