mathematics

E series of preferred numbers

E series of preferred numbers is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand E series of preferred numbers rather than just read about it. In short: 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 logarithmic value "steps" per decade.

Key takeaways

E series of preferred numbers belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect E series of preferred numbers to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of E series of preferred numbers from memory before moving on to harder problems.

Reference excerpt

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 logarithmic value "steps" per decade. 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, such as fuses, are either specified by the Renard series or are defined in relevant product standards, such as IEC 60228 for wires.

History During the Golden Age of Radio (1920s to 1950s), numerous companies manufactured vacuum-tube–based AM radio receivers for consumer use. In the early years, many components were not standardized between AM radio manufacturers. The capacitance values of capacitors (previously called condensers) and resistance values of resistors were not standardized as they are today. In 1924, the Radio Manufacturers Association (RMA) was formed in Chicago, Illinois by 50 AM radio manufacturers to license and share patents. Over time, this group created some of the earliest standards for electronics components. In 1936, the RMA adopted a preferred-number system for the resistance values of fixed-composition resistors. Over time, resistor manufacturers migrated from older values to the 1936 resistance value standard. During World War II (1940s), American and British military production was a major influence for establishing numerous standards across many industries, especially in electronics, where it was essential to produce high quantities of standardized electronic components to build military devices, such as wireless communications and jammers, radar and jammers, LORAN radio navigation homing receivers for aircraft, ASDIC (sonar) for submarine navigation and detection, test equipment, and more. Later, the mid-20th century baby boom and the invention of the transistor kicked off demand for consumer electronics goods during the 1950s. As portable transistor radio manufacturing migrated from United States towards Japan during the late 1950s, it was critical for the electronic industry to have international standards. After worked on by the RMA, the International Electrotechnical Commission (IEC) began work on an international standard for preferred values 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:

IEC 63:1952 (aka IEC 60063:1952), first edition, published 1952-01-01. IEC 63:1963 (aka IEC 60063:1963), second edition, published 1963-01-01. IEC 63:1967/AMD1:1967 (aka IEC 60063:1967/AMD1:1967), first amendment of second edition, published 1967. IEC 63:1977/AMD2:1977 (aka IEC 60063:1977/AMD2:1977), second amendment of second edition, published 1977. IEC 60063:2015, third edition, published 2015-03-27.

Overview The E series of preferred numbers was chosen such that when a component is manufactured it will end up in a range of roughly equally spaced values (geometric progression) on a logarithmic scale. Each E series subdivides each decade magnitude into steps of 3, 6, 12, 24, 48, 96, and 192 values, termed E3, E6, and so forth to E192, with maximum errors of 40%, 20%, 10%, 5%, 2%, 1%, and 0.5%, respectively. The E192 series is also used for 0.25% and 0.1% tolerance resistors. Historically, the E series is split into two major groupings:

E3, E6, E12, E24 are subsets of E24. Values in this group are rounded to 2 significant figures. E48, E96, E192 are subsets of E192. Values in this group are rounded to 3 significant figures.

Formula The formula for each value is determined by the m-th root, but unfortunately the calculated values don't match the official values of all E series.

V n = ⌈ 10 n m ⌋ {\displaystyle V_{n}=\left\lceil {\sqrt[{m}]{10^{n}}}\right\rfloor }

where:

⌈ x ⌋ {\displaystyle \lceil x\rfloor } denotes x {\displaystyle x} rounded to the nearest whole number,

V n {\displaystyle V_{n}} is rounded to 2 significant figures (E3, E6, E12, E24) or 3 significant figures (E48, E96, E192),

m {\displaystyle m} is an integer of the E series group size (3, 6, 12, 24, 48, 96, 192),

n {\displaystyle n} is an integer of { 0 , 1 , . . . , m − 1 } . {\displaystyle \{0,1,...,m-1\}.}

exceptions: The official values for E48 and E96 series match their calculated values, but all other series (E3, E6, E12, E24, E192) have one or more official values that don't match their calculated values (see subsets sections below).

E24 subsets For E3, E6, E12, and E24, the values from the formula are rounded to 2 significant figures, but eight official values (shown in bold and green) are different from the calculated values (shown in red). During the early half of the 20th century, electronic components had different sets of component values than today. In the late 1940s, standards organizations started working towards codifying a standard set of official component values, and they decided that it wasn't practical to change some of the former established historical values. The first standard was accepted in Paris in 1950, then published as IEC 63 in 1952. The official values of the E3, E6, and E12 series are subsets of the following official E24 values.

… excerpt ends here. Continue reading the full article.

Illustrations

Worked examples

Example 1 — a first encounter with E series of preferred numbers

Start with the simplest possible case. Write down what E series of preferred numbers claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to E series of preferred numbers before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about E series of preferred numbers ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of E series of preferred numbers

In research: E series of preferred numbers appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses E series of preferred numbers in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: E series of preferred numbers is common in secondary-school and first-year university syllabi. It links to neighbouring topics Electrical components, Industrial design, Logarithmic scales of measurement, so understanding it makes those chapters shorter.
In everyday life: Look for E series of preferred numbers outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study E series of preferred numbers in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what E series of preferred numbers means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain E series of preferred numbers out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is E series of preferred numbers in simple terms?

Why does E series of preferred numbers matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study E series of preferred numbers?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on E series of preferred numbers.