Is there a way when this form is submitted, that any quantity that is zero is ommited?

Here is the form, thanks!

https://form.jotform.com/73458883678276

You can remove the zero default value:

So, if the form is submitted, those field will be submitted empty, and they will not show in the notification if you have set to hide empty fields: https://www.jotform.com/help/256-How-to-Hide-Empty-Fields-on-Email-Alerts 

You can also hide empty fields in your submissions page: https://www.jotform.com/help/269-How-to-View-Form-Submissions 

Let us know if you need more helpl