Before learning of the historical circumstances, the Doctor speculated that they had travelled 10,000,000 years into the future. However, with the Earth being swallowed up by the Sun, it is more likely that this time period is c. 5,000,000,000 AD. An alternative explanation is that Earth was not completely destroyed in The Ark, and that the National Trust's renovations were more extensive than the Doctor told Rose.
If all of these suppositions are correct, then the segments are not equal length like years or centuries, but rather referring to historical periods, much as we refer to periods like "The Stone Age" or "The Renaissance".
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