E series of preferred numbers

The E series is a system of preferred numbers (also called preferred values) derived for use in electronic components. It consists of the E3, E6, E12, E24, E48, E96 and E192 series, where the number after the 'E' designates the quantity of value "steps" in each series. Although it is theoretically possible to produce components of any value, in practice the need for inventory simplification has led the industry to settle on the E series for resistors, capacitors, inductors, and zener diodes. Other types of electrical components are either specified by the Renard series (for example fuses) or are defined in relevant product standards (for example IEC 60228 for wires). 
History.
In the early 20th century, capacitor (previously called condenser) and resistor value increments were different than today. 
American and British military production during World War II was a major influence for establishing common standards across many industries, especially in electronics, where it was essential to produce large quantities of standardized electronic parts very quickly. Later, the post–World War II baby boom and the invention of the transistor kicked off demand for consumer electronics goods during the 1950s. As transistor radio production migrated towards Japan during the 1950s, it was critical for the electronic industry to have international standards. 
Over time, components evolved towards common values, then based on some of these existing conventions, as worked on by the Radio Television Manufacturers Association (RTMA), the International Electrotechnical Commission (IEC) began work on an international standard in 1948. The first version of this IEC Publication 63 (IEC 63) was released in 1952. Later, IEC 63 was revised, amended, and renamed into the current version known as IEC 60063:2015.
IEC 60063 release history:
Overview.
The E series of preferred numbers were chosen such that when a component is manufactured it will end up in a range of roughly equally spaced values on a logarithmic scale. Each E series subdivides each decade magnitude into steps of 3, 6, 12, 24, 48, 96, 192 values. Subdivisions of E3 to E192 ensure the maximum error will be divided in the order of 40%, 20%, 10%, 5%, 2%, 1%, 0.5%. Also, the E192 series is used for 0.25% and 0.1% tolerance resistors.
Historically, the E series is split into two major groupings:
Since the electronic component industry established component values before standards discussions in the late-1940s, they decided that it wasn't practical to change the former established values. These older values were used to create the E6, E12, E24 series standard that was accepted in Paris in 1950 then published as IEC 63 in 1952. Eight of the E24 values do not match the following formula.
The formula for each value is determined by the n-th root:
For E3 to E24, the values are rounded to 1 trailing digit. For unknown historical reasons, eight older industry values (shown in bold) are different from the calculated values.
For E48 to E192, the values are rounded to 2 trailing digits.
E3.
The E3 series is rarely used, except for some components with high variations like electrolytic capacitors, where the given tolerance is often unbalanced between negative and positive such as or , or for components with uncritical values such as pull-up resistors. The calculated tolerance for this series gives ( − 1) ÷ ( + 1) = 36.60%. While the standard only specifies a tolerance greater than 20%, other sources indicate 40% or 50%. Currently, most electrolytic capacitors are manufactured with values in the E6 or E12 series, thus E3 series is mostly obsolete.
E24 vs. E48, E96, E192.
Since some values in the E24 series do not exist in the E48, E96 and E192 series, resistor manufacturers have added the missing E24 values to some of their 1%, 0.5%, 0.25%, 0.1% tolerance families. This allows easier purchasing migration between different tolerance parts. This type of combination is noted on resistor datasheets and webpages as "E96 + E24" and "E192 + E24".
Comparison of E24 vs. E48 values:
Comparison of E24 vs. E96 values:
Comparison of E24 vs. E192 values:
Examples.
If a manufacturer sold resistors with all values in a range of 10 ohms to 10 megaohms, the available resistance values for E3 through E12 would be:
If a manufacturer sold capacitors with all values in a range of 10 pF to 1000 μF, the available capacitance values for E3 and E6 would be:
Lists.
List of values for each E series: