This is quite "normal" and I experience it with my blends on a friend's 3D printer as well, since different softwares and file formats store and interpret mesh data differently.
Let's say Blender stores the value 0.51 for the length and your Blender Scene Properties > Units are set to Unit System "Metric" and for the Unit Scale "1.000000" then it tells Blender that the length is 0.51 meters.
Now another software only gets this value 0.51 but no information like scene properties, and if it usually works with 1 centimeter as scale base then this value is interpreted as 0.51 centimeters.
All in all, the Scene Properties setting for the Unit System and Unit Scale also reveal what this size in Blender really is: a more or less arbitrary choice. I think some physics simulations use these real-world scales for calculating more realistic results.
No matter it's no real size - in the end, if you look at the default cube: if you have Blender set to "Metric" and a Unit Scale of 1, then the cube is 2m * 2m * 2m.
But without changing anything on the cube itself, no scaling in Object Mode or Edit Mode, as soon as you change the Unit Scale to 0.1, the cube suddenly is smaller, 0.2m * 0.2m * 0.2m.
Or changing the Unit System to "None", the cube is 2 * 2 * 2 without any dimension. So what you can do (since you know the printing software scales the mesh down by factor 100), you could set the Unit Scale to 0.01, in this case all dimensions of your object will be shown in the size at which the printing software interpretes it.