Keeping it all in the same units until the end here:
1 millionth of 1 meter = (1 / 1,000,000)m = (1e-6m)
1 millionth * 100 = 100 millionths => (1e-6m) * 100 = (1e-4m) = 100 millionths
(1e-4m) = .0001m | 1m = 1000mm => .0001m*1000 = .1mm
I am to used to people saying 100 millionth of a meter to mean 10 nm or 0.01 µm which would have looked insane if I had written that.
Aka 100 millionth vs 100 millionths
Keeping it all in the same units until the end here:
1 millionth of 1 meter = (1 / 1,000,000)m = (1e-6m)
1 millionth * 100 = 100 millionths => (1e-6m) * 100 = (1e-4m) = 100 millionths
(1e-4m) = .0001m | 1m = 1000mm => .0001m*1000 = .1mm