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E Series Preferred Numbers

The logarithmic scale

Electrical components come in logarithmic values that can be combined in series and parallel to create any desired value.
These values are in percentage increases of 40%, 20%, 10% or 5% and classified by their number of subdivisions per decade (x10).

E3 = 3 steps per decade with 40% tolerance per step.
E6 = 6 steps per decade with 20% tolerance per step.
E12 = 12 steps per decade with 10% tolerance per step.
E24 = 24 steps per decade with 5% tolerance per step.
etc..

Some manufacturers produce components that are in even smaller incremental steps, I've seen down to E192 (0.5%). But those values are rare. Normally when you need that level of precision you no longer use fixed values and opt for something tunable like trimmers and rheostats.

Below are the values for the E series from E3 thru E24.

E Series Chart
True Value E24 E12 E6 E3
10.0000 10 10 10 10
11.0069 11
12.1153 12 12
13.3352 13
14.6780 15 15 15
16.1560 16
17.7828 18 18
19.5734 20
21.5443 22 22 22 22
23.7137 24
26.1016 27 27
28.7298 30
31.6228 33 33 33
34.8070 36
38.3119 39 39
42.1697 43
46.4159 47 47 47 47
51.0897 51
56.2341 56 56
61.8966 62
68.1292 68 68 68
74.9894 75
82.5404 82 82
90.8515 91

E Series has many uses

E Series numbers also work well for things outside of just electronic component values. I have used them in everything from carpentry to software design and find that for a numbering system, it has the best distribution when dealing with a wide order of magnitude. Things naturally graph out in logarithmic fashion if they apply across a large enough range. 

 _______________________________________       _______________________________________ 
┃"""|"""|"""|"""|"""|"""|"""|"""|"""|"""┃     ┃"""|"""|"""|"""|"""|"""|"""|"""|"""|"""┃
┃   1   2   3   4   5   6   7   8   9   ┃ v.s ┃   1   2.2 4.7 10  22  47  100 220 470 ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛     ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

Why use any preferred numbers at all?

Say you are manufacturing cardboard shipping boxes. The various things you can put into a box could be of any size or shape. So it is reasonable at first to think something like "let's make boxes in all sizes increasing in one inch increments". The problem you run into very quickly is the massive number of different box dimensions you now have to make and keep in inventory.

While going from a 3x3x2" box to a 4x3x2" makes sense. Having a box that is 72" inches across and also producing a 73" inch box doesn't make much sense. It would make more sense to manufacture less variations of boxes in standard "preferred" sizes like: 6x6x3, 10x6x4, etc... and have your customers select the closest box that fits.

Once you start looking, you will find preferred numbers everywhere.
There is a reason why the money in your wallet is in increments of $1, $2, $5, $10, $20, $50 and $100 (called the 1-2-5 series). Because again it doesn't make sense to print dollar bills for all values between $1 and $100. What use is a $43 dollar bill? Instead you can use combinations of values from the series to make all other values: $43 = $20 + $20 + $2 + $1. 

    ┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓    
    ┃#######====================#######┃    
    ┃#(2)*UNITED STATES OF AMERICA*(2)#┃    
    ┃#**          /===\   ********  **#┃    
    ┃*# {G}      | ( ) |             #*┃    
    ┃#*  ******  | /v\ |    T W O    *#┃    
    ┃#(2)         \===/            (2)#┃    
    ┃##=========TWO DOLLAR===========##┃    
    ┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

...and yes there is a $2 bill. It is not as useful as a $5 or $10 so they don't circulate as well. People like to collect them for this reason and has inspired an urban legend of bad luck. But that is another story for another day.

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