A school received 2 orders of new chairs. The first order contained 180 chairs. The second order contained 204 chairs. Each of the 17 classrooms received the same number of chairs. How many chairs will be put in storage as extra chairs?

To find how many chairs will be put in storage as extra chairs, we first need to calculate the total number of chairs received and then determine how many can be evenly distributed among the classrooms.

1. Calculate the total number of chairs: \[ \text{Total chairs} = 180 + 204 = 384 \]

2. Next, find out how many chairs each of the 17 classrooms can receive: \[ \text{Chairs per classroom} = \frac{384}{17} = 22.5882 \] Since we cannot have a fraction of a chair, we will only distribute whole chairs. We calculate how many whole chairs can be distributed to each classroom: \[ \text{Whole chairs per classroom} = 22 \]

3. Now, calculate the total number of chairs distributed: \[ \text{Total distributed chairs} = 22 \times 17 = 374 \]

4. Finally, find out how many chairs remain as extra in storage: \[ \text{Extra chairs} = 384 - 374 = 10 \]

Thus, the number of chairs that will be put in storage as extra chairs is \( \boxed{10} \).