番号 and 記号: identifying numbers and symbols
Distinguish identifying information from quantities when reading numbers and symbols.
An identifying number
番号 (ばんごう) means an identifying number. 「箱に番号を付けました」 means numbering the boxes.
「番号の小さい順に並べてください」 requests ordering by ascending number, not by the objects' physical size.
A meaningful symbol
記号 (きごう) means symbol or sign. 「地図の記号を調べました」 means checking the symbols on a map.
「丸い記号が入口を表します」 gives a particular legend in which a round symbol marks an entrance. Do not generalize it to every map.
Preserving the written identifier
「番号の前に記号を付けてください」 requests a symbol before the number. 前 here means the front of the written sequence.
When copying identifiers, do not arbitrarily remove leading zeros or symbols. First distinguish a quantity for calculation from a label used to locate an item.
Does 「番号の小さい順」 order boxes by physical size?
Show the answer and why
No. It orders their identifying numbers; physical size is separate.