I'm trying to help my daughter with the concept of lower and upper bounds of a number when given a specific accuracy, but I'm starting to realise how many holes there are in my own knowledge!
For a specific number of decimal places this is straightforward:
$x=1.23$ to 2 decimal places.
Therefore: $1.225 \le x \lt 1.235$
Equally, for numbers given to a number significant figures it is much the same. Eg:
$x=99$ to 2 significant figures
Therefore: $98.5 \le x \lt 99.5$
Or $x=110$ to 2 significant figures
Therefore: $105 \le x \lt 115$
However, this is what I can't figure out:
$x=100$ to 2 significant figures.
Since anything between 100 and 105 rounded to 2 significant figures would be 100, logically the upper bound is 105.
On the other hand, the lower bound cannot correspondingly be 95 because 95 to 2 significant figures is 95!
Therefore, should it be that in this case:
$99.5 \le x \lt 105$? If so, that rather lacks the symmetry I had expected.