You're very close! While the Milky Way is about 100,000 light-years wide, it's not quite accurate to say it's that wide at its nucleus. Here's why:

* The nucleus is much smaller than the entire galaxy. The nucleus, also known as the galactic bulge, is a densely packed region in the center of the Milky Way. It's where the supermassive black hole Sagittarius A* resides.

* The nucleus is estimated to be about 10,000 light-years across. This is significantly smaller than the overall diameter of the galaxy.

So, to complete your statement, you could say:

"At its nucleus the Milky Way Galaxy is about 100,000 light-years wide and its nucleus is about 10,000 light-years across."