FAQ indicates you'll get partial stars for the cents.
"What will happen in the new program if I spend an uneven amount? Do I get credit for the change?+
Yes, your change counts towards partial Stars. We’ll keep track of all your partial Stars and apply them to your total Stars.
For example, if you spend $6.20 (i.e., not including tax, tips, alcohol or other exceptions), you will earn 12.40 Stars.
The .40 is not always visible (we like to keep things simple), but you can always view your Stars and purchase history at starbucks.com/rewards or in the mobile app."