@Welbog said:
10cm is the same as 10.000cm
To a scientist, engineer or mathematician, maybe, but not to other people.
Go to a timber yard and ask for a bit of wood 10cm long and you'll get one about that long. Ask for one 10.000cm long, and you won't. If they are intelligent they'll refuse to serve you because they can't guarantee they'll be able to give you a piece exactly that long. If they're not so intelligent they'll give you a piece of wood which doesn't meet your requirements.
If UPS ask you how big a parcel is, do you say '10cm by 20cm by 5cm' or do you say '10.126cm by 19.766cm by 5.002cm'? Most people would say the former, even if the latter was more accurate. They also wouldn't say '10cm by 20cm by 5cm with a +/-5% error'. If you are the sort of person who would, then I pity any of your friends...
So, if you go to a shipping website which does conversion, and it says: 'enter the width of the parcel in whichever units you want' and you enter '10cm', then in the confirmation it says:
Parcel width: 3.93700787 inches
would you accept that confirmation? I'm not sure I would, because I couldn't check that my parcel was really 3.93700787 inches wide (says I, being careful not to use the word 'package' on a techie website when talking about measurements...) If it said 'Parcel width: 4 inches' I'd still have concerns, although less so. I'd actually want it to be confirmed back in the units of measurement that I specified.
Also I wouldn't expect the shipping website to ask me for the width of the parcel with an error specification, otherwise it would get confusing for lots of people.
Note that I am just talking about 'normal' conversions for 'normal' people. If you get into measurements where you would be talking in millimeters or 32nds of an inch or smaller, then, yes, be as precise as you want in your conversions.
(PS - I guess I'm trying to say that, literally and mathematically, yes, 10cm is the same as 10.000cm, but it has a 'meaning' beyond that. The precision that you specify implies a required accuracy/precision. You can make this explicit by extra words such as 'exactly', 'approximately', 'about', 'precisely' or by specifying an error range, but if you don't then, in normal speech, there is an implication of the error range).