That's not how errors add up, it's nonlinear. You have to take the sum of squares. So in your case, it wouldn't be 10 * 0.01 = 0.1, but sqrt(10 * 0.01^2) = 0.032, which is less than one third of a tenth.
I provided a "worst case", not statistical, example.
For those who want an example, calculator, and demo see: https://www.smlease.com/entries/tolerance/tolerance-stackup-...
NB: using disks like the site does provides a clearer example.
A safe example is bike chain. If each one is 1 inch +- 0.01", if every single one is +0.01" then ten links will be long by a tenth of an inch. And might pass QC on the bike when pedaled by hand- but it'll fall off when somebodies full bodyweight and 100hrs of wear is out into it.