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A Monte Carlo numerical simulation is performed to clarify the reason why an atomic resolution microscope such as a scanning tunneling microscope (STM) cannot give accurately a ppm (parts per million) concentration of elements quantitatively. A relation between the sampling amount and the accuracy has been found. At least 10 9 atoms are needed to be sampled in order to discriminate the 49 and 50 ppm elemental concentrations. This Monte Carlo result has also been applied to the elemental analysis methods such as ICP-AES (inductively-coupled plasma atomic emission spectrometry) and TXRF (total reflection X-ray fluorescence) to clarify the appropriate amount of sampling amount for required precision of quantitative elemental analysis.