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Money measurement concept is where we only account for items that can be measured in monetary terms......hence when accounting for costs, we wont account for non-monetary items.
Monetary is something that is related to money or currency. Non-monetary is the opposite and usually means that something can't be expressed in financial terms.
Eg Your computer has a monetary value (ie what it costs or is worth in financial terms) and it can also have a non-monetary value (ie how much you like it or sentimental value).