There are at least 2 ways to do it in 8 cuts. The simplest is:
1st cut in halves, 2 x 50cm pieces
2nd cut in quarters, 4 x 25 cm pieces
3rd cut cut 1cm off, 4 x 24 cm pieces & 4 x 1cm pieces
the 4 x 1cm pieces are done, set them aside
4th cut creates 4 x 16cm pieces and 4 x 8 cm pieces -cut each 24cm piece 1/3 & 2/3
5th cut only on 4 x 16cm pieces, creating 8 x 8 cm pieces
we now have 12 x 8cm pieces (and 4 finished 1cm pieces set aside)
6th cut - all 8cm pieces in half gives us 24 x 4cm pieces
7th cut - in half again, now we have 48 x 2cm pieces
8th cut - in half again, we now have 96 x 1cm pieces, plus the 4 x 1cm pieces set aside in step 3
Is a total of 100 1cm pieces created in 8 cuts.
I found another way to do it in 8 pieces, very complicated to describe. It's the same through step 4. Then each remaining piece is either 16 or 8cm, and cut in half again and again until it reaches 1cm and is set aside.
This second method can be proven to be the minimum number of cuts, since every piece that is not 1cm long is cut every time the knife is used. So, although there are multiple ways to do it in 8 slices, I think 8 slices must be the minimum possible.
It is interesting to think of this problem in terms of prime factors.
The prime factoring of 100 is 2 x 2 x 5 x 5.
The cutting solution is to slice in half whenever you can, so 2 slices creates 4 x 25cm pieces (or 2x2 pieces, each 5x5 in length)
by trimming the 25 inch pieces to 24cm and 1cm pieces, we can set the 1cm pieces aside.
Then we have to finish the remaining 4 x 24cm pieces.
The prime factoring of 24 is 2 x 2 x 2 x 3
At this point, cutting in thirds gives pieces that are all a length of powers of 2 (8cm or 16cm each), and any way of cutting these in 4 or fewer slices finishes the job.