To write down something is to put it on paper so you will not forget it. Write down the number, write down what he said, write it down.
The down adds the sense of committing it somewhere permanent rather than merely writing. In accounting, to write down an asset is to reduce its recorded value, which is a separate trade sense.
1phrasewrite downTo put words on paper so you will not forget them.
“Write down the number before you forget it.”
write down is a phrase.
Also accepted in games: note down, jot down
Practised in Phrasal Verbs