The first number is the amount of chromium that is contained in the stainless, i.e., 18 is 18% chromium. The second number is the amount of nickel, i.e., 8 stands for 8% nickel. So 18/8 means that this stainless steel contains 18% chromium and 8% nickel. 18/10 is 18% chromium and 10% nickel. The higher the numbers the more corrosion resistant the material. 18/0 is a misleading designation. Both 18/8 and 18/10 contain nickel and are part of the grade family "300 series" stainless. 18/0 means that there is 18% chromium but zero nickel. When there is no nickel the stainless grade family is the "400 series". 400 series are not as corrosion resistant as the 300 series and are magnetic, where the 300 series are non-magnetic.
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What is the difference between 18/8 and 18/10 stainless steel?