Some paper plates have a poly-coating which is a type of plastic. This product is unfortunately landfill/trash, since the product contains both plastic and paper. However, there are also paper products that have a wax coating. These products are actually compostable because the wax coating can be broken down along with the paper.
Both products look and feel similar. Nevertheless, there is a way to tell the difference. If when scratching the paper plate the coating comes off, then it is a wax coated plate and can be composted. When you scratch and nothing comes off, the paper plate has a poly-coating and must be placed in the landfill.
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