220, 330 … 470? Why we have the resistor values we do

The first thing is that we rarely need exact resisitor values in electronics. We often need one 'around 200 ohms' or 'to keep the current between 10ma and 20ma'. The series of values we have is useful not because we need exactly these values, but because one of these values is usually good enough.

Likewise, when making electronics, there's a tolerance. This is usually specified on the product. It specifies the degree to which a component can be 'out' by. A 220 ohm resistor with a 5% tolerance will be between 209 and 231 ohms. 5% might not be considered that accurate these days (but still easily accurate enough for many uses). Years ago, 20% was also a common tolerance, where a 220 ohm resistor with a 20% tolerance might be between 176 and 264 ohms. A 330 ohm resistor with a 20% tolerance will be between 264 and 394 ohms.

Did you notice that? At 20% tolerance, there's a cut off at 264 ohms between 220 ohm resistors and 330 ohm resistors. Likewise, the cut off between 330 ohm and 470 ohm is about 380ohms (about because there's a bit of rounding in the numbers).

This sequence of numbers where each is a certain percentage above the last is known as the E series. It's useful for electronics for two reasons. It means that you'll always be able to get a component within a certain percentage of your ideal components, and it means that if you manufacture comonents with random values, they'll always fit into a particular tolerance bucket (this, hopefully, isn't a big deal with modern manufacturing techniques, but we established these standards decades ago).

There's more details on the maths behind this series of numbers on wikipedia at https://en.wikipedia.org/wiki/E-seriesofpreferred_numbers.

They might seem a little unusual at first, but you'll quickly find youself thinking automatically in terms of this sequence of numbers.