The way you have it now is better. Technically, it is optional since you're being definitive.
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AnonymousIs by optional?The temperature has dropped (by) one degree.Yes, it's optional.
AnonymousCould you tell me if the 2 words are optional?They are optional. However, in my opinion, in the first case it's better to include 'after', and in the second case it's better to omit 'amount'.