Rachel's Problem

Is it true that $99^n$ has 2n digits and $999^n$ has 3n digits? Investigate!
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative


Is it true that $ 99^n $ has $ 2n $ digits and $ 999^n $ has $ 3n $ digits? Investigate!

(This problem was inspired by Rachel Galley's work on the problem called Giants in the June 1999 Six.)