First, let's determine the total amount of money Chloe has in her wallet.
Three $10 bills is a total of $3 \times 10 = $30.
Eight quarters is a total of $8 \times 0.25 = $2.
The total amount of money Chloe has is $30 + $2 = $32.
Since the hoodie is priced at $32.75, Chloe is $0.75 short.
Since each dime is worth $0.10, Chloe needs $0.75/$0.10 = 7.5 dimes.
Since Chloe cannot have a fraction of a dime, she needs to have at least 8 dimes.
Therefore, the smallest number of dimes she needs is $\boxed{8}$.
The answer is: 8
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
Chloe wants to purchase a hoodie priced at $32.75. After checking her wallet, she realizes she only has three $10 bills, eight quarters, and an unknown number of dimes. What is the smallest number of dimes she needs in order to have enough to pay for the hoodie?

### Answer:
