Many small companies have difficulty growing because the number of orders becomes too large to handle.
Should I use become or becomes in this sentence? I don't know, but the sentence feels a little odd to me.
Many small companies have difficulty growing because the number of orders becomes too large to handle.
Should I use become or becomes in this sentence? I don't know, but the sentence feels a little odd to me.
Many small companies have difficulty growing because the number of orders becomes too large to handle.
In your sentence, you need to see what exactly is becomes describing. Whether you should use "become" or "becomes" depends on what the word intends to describe- number or orders.
because the number of orders becomes too large to handle
Here, becomes refers to number. Number is used as singular here, so you should use becomes.
When you intend to refer to orders instead, that is when you would use become, as in this (hypothetical) example:
Many small companies have difficulty growing because their orders become too large to handle.
Also take a look at this and this. They describe some basic rules to help deal with similar sentences.
Many small companies have difficulty growing because the number of orders becomes too large to handle.
If you cross out "of orders," which is a prepositional phrase modifying "number," you see that the verb become is referring to number. Number is singular, so you would use becomes. "Of orders" can be safely ignored because it is a modifier:
Typically the modifier can be removed without affecting the grammar of the sentence. (http://en.wikipedia.org/wiki/Grammatical_modifier)