Cent vs. centaine
The French words cent and centaine both relate to the number 100, but they are not interchangeable. Cent is a cardinal number used for exact counting, while centaine is a noun used to express an approximate quantity.
Cent
A1Cent is the cardinal number for one hundred. It is used to specify an exact quantity, whether in counting, stating a price, or giving a date. It becomes cents in the plural for round hundreds (e.g., deux cents), but remains cent when followed by another number.
Ce pantalon coûte cent euros.
(These pants cost one hundred euros.)
Le marathon fait quarante-deux kilomètres et cent quatre-vingt-quinze mètres.
(The marathon is forty-two kilometers and one hundred and ninety-five meters.)
Il y a plus de quatre cents ans, ce château a été construit.
(This castle was built more than four hundred years ago.)
Le livre contient exactement deux cent trente pages.
(The book contains exactly two hundred and thirty pages.)
Vingt pour cent de la population a voté.
(Twenty percent of the population voted.)
Centaine
A2Centaine is a feminine noun that means a group of about a hundred or a hundred or so. It indicates an approximation, not an exact number. As a noun, it is always followed by de or d when it precedes another noun, and it can be pluralized ('des centaines) to mean hundreds of.
Une centaine de personnes ont assisté au concert.
(About a hundred people attended the concert.)
J'ai reçu une centaine de messages pour mon anniversaire.
(I received a hundred or so messages for my birthday.)
Des centaines d'oiseaux volaient au-dessus du lac.
(Hundreds of birds were flying over the lake.)
Il a fallu une bonne centaine d'heures pour terminer le projet.
(It took a good hundred hours to finish the project.)
Le village se trouve à une centaine de kilomètres d'ici.
(The village is about a hundred kilometers from here.)
Summary
In short, use cent for the exact number 100 and its multiples (200, 350, etc.). Use centaine for an approximate quantity, meaning about a hundred. The key grammatical signal is that centaine, being a noun, is followed by de or d before another noun, whereas 'cent is not.