How long is a piece of string?

Logic Level 3

Bernice has a long piece of string. She cuts it into two pieces, then cuts each piece into two each again, then cuts each new piece into two each once again a third time, so that she's left with 8 pieces of string. The point at which she cuts a piece of string is never more than 2cm from the exact center of each piece being cut.

What is the greatest possible difference between the longest and shortest pieces of string after she has finished cutting?

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