Learn French: Il ajoute la moitié d'un centimètre pour l'ourlet.

In English, we say "half a centimeter," but in French, la moitié is a noun meaning "the half." To connect it to the noun that follows, you must use de (of). So, the French sentence literally says "the half of a centimeter."

Could I use demi instead of la moitié in this sentence?

Yes, you could completely rephrase it to say Il ajoute un demi-centimètre. Demi acts as an adjective here, while la moitié is a noun. Both are very common and natural ways to express "half," but you must use de when using the noun form.

Why is it d'un and not de un? I thought we don't drop the 'e' before numbers.

You are thinking of a specific rule for numbers like huit (eight) and onze (eleven), where you never drop the 'e' (so it's de huit, never d'huit). However, for the number un (one), you always drop the 'e' in de to avoid two vowel sounds clashing, making it d'un.

Is the 't' pronounced at the end of ourlet?

No, the final 't' in ourlet (hem) is silent. The end of the word rhymes with the English word "play".