I was reading the Wikipedia entry for E-series resistor values, and I decided to graph the values on a log plot. The plot shows the values nearly evenly spaced, which makes sense because adjacent values are supposed to be related approximately by the factor where N is the resistor series (E6, E12,...,E192).
If I then plot the tolerance range for each value in the E6,E12, E24 ranges, I see overlap for each standard resistor value with the adjacent value – this makes sense because every resistor made can then be used. Here is my plot, which is crude but makes the point – note that I zoomed in a bit, so all values are not shown.
However, if you plot the range of values for the E48, E96, and E192 ranges, I see small gaps. This means that every resistor made may not fall into a standard 2% tolerance value. I show my plot for the E48 resistor series below. I zoomed in quite a bit to make things a bit clearer.
I can also demonstrate that the gaps exist using algebra, but I thought the charts illustrate the issue better.
Are there really gaps in the 2% standard resistor values?