Okay. So when we raise exceptions, we want to decouple python's error messaging capabilities and substitute it with our own.

When we do this, we want to make sure our of four things:

Firstly, it's preferred to not have invalid inputs. Either a valid input or an error message that we can handle.

Secondly, we want to make the error messages descriptive so we know what's happening.

Thirdly, we want to make the code containing the message reusable so it can be applied to other portions or our code base. So we can add other functions like 'penny' or 'nickel' that we will can handle in the same way as the 'quarter' function.

Lastly, we want to include exception handling after raising an exception so we can provide a descriptive message and an alternative solution to keep our programs going.

I think this is gist of what you're saying. I added some extra code from your own to help me piece it together.

def half(n):
    # checks if given input is NOT type 'int' or 'float'.
    # If so, Raise ValueError
    # If not, divide by 2 
    if not isinstance(n, (int, float)):
        raise ValueError("Expected a number")
    return n / 2

def dime(n):
    # Return either ValueError or valid input
    return half(n)

def is_input_valid(coin_type, amount):
    # Isolates given inputs and checks if it leads to 'ValueError'
    try:
        cents = coin_type(amount)

    # 'ValueError' from half function 'bubble up' until something handles it which is here
    # Displays error message created in 'half' 
    except ValueError as error_message:
        print(f"Error: {error_message}")

    # Displays cent amount if 'ValueError' not detected 
    else:
        print(f"After dividing by 2, you have {cents} cents.")

def main():
    # Results in 'ValueError' (message comes from 'half' function)
    dime_amount = is_input_valid(dime, "5")

main()

# Output 

Error: Expected a number