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I'm sorry if this has been asked, as it's a simple question, but I haven't found it.

Is there any reason why capacitors are built in so fixed values? For any other components the manufactured value are round numbers, for example resistors 100 Ohm - 1 kOhm - 10 kOhm - ... but capacitors come in weirder numbers, specifically, why can you find multiples of 4.7? is there anything special about that number? is there any normal circuit that goes on everything that needs a capacitance like that?

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Look at a supplier catalogue for your resistors. They too are available in sizes of 2.7, 3.3, 6.8, 8.2 just like their capacitor cousins. Inductors follow this pattern as well.

The sizes of components progress through the a series from 1-10 in a way that the neighbor values are within step sizes of 5%, 10% or 20%. You can read a nice write up in the concept of preferred values here. Look specifically for the E-series as it relates to electronics.

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