Upper and Lower bounds Exam style question Ewan uses a piece of wood 0.8m long, correct to 0.02m, to make a shelf. He then marks out the shelf every 10cm. He finds he has space at the end.
What is the maximum length the space could be.
So I know that 0.79m ≤ length of wood < 0.81m
But seeming the length of wood could be 0.799999999999m recurring, what would you say the meximum length the space could be. Doesn't really seem right just saying < 10cm space but I'm not sure what else to put. If I say 9.9cm recurring then that's technically the same as saying 10cm anyway
 A: This question is more tricky than it seemed at first and all credit to Clayton for pointing out the subtleties within it.
The lower bound on the length of the wood is 0.78 m
The upper bound on the length of the wood is 0.82m
That is the length of the shelf in metres is,
$$0.78  \leq length \lt 0.82$$
Ewan's 10cm measurement is also subject to a measurement error but for now assume it's exact.
So, Ewan measures out exactly 7 lots of 10 cm or 0.7 m
What Clayton pointed out was that the shelf could be 0.79 m long, or 0.799 m long or 0.7999$\dots$ which has an upper bound of 0.8 m.
This in turn means that the length left has an upper bound of 10 cm
So the maximum length of the length left has an upper bound of 10 cm corresponding to the worst case situation of the shelf having a length with an upper bound of 0.8 m
Finally, let's return to Ewan's 10cm measurement. I would argue that, now that the situation is understood, it's obvious that a small error in what he measures as 10 cm is not going to alter the answer...
