Category Archives: Metric System in Popular Culture

Lies, Damned Lies, and Scientific Notation

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By The Metric Maven

Bulldog Edition

My first extended use of scientific notation was in my introductory chemistry class, Chem 147, at a large university. Anyone who has taken a chemistry class will certainly remember 6.022 x 1023 as Avagardro’s number. It appears to be nice, compact and expressive. I was certainly beguiled with scientific notation as I watched my professor manipulate magnitudes large and small with apparent ease. The numbers would cause one to think, “that’s really big”, or “that’s really small.” It all seemed so nice and orderly—and useful. The one question I did not ask was: “what is the actual relation of the magnitudes expressed on the blackboard to the physical world?”

What happened next did not really provide an answer, but introduced another question. I had purchased a Hewlett-Packard RPN calculator, which has a beautifully written manual. It was while perusing the manual that I ran across settings for the display. I could have fixed, scientific and engineering notation displayed. Engineering notation?—I had not heard of it. It was never mentioned in High School. I then saw a small table which showed it. Scientists use the term order of magnitude to describe a power of ten. This is the superscript used in scientific notation. Engineering notation had categorized scientific notation into groups which differ by three orders of magnitude. It automatically eschews the prefix cluster around unity (i.e centi, deci, deca and hecto). In a millisecond I was enamored with engineering notation, but it would be many, many years before I really understood the beauty and utility of it.

The current set of three magnitude multipliers is eight. This group spans a range from 103 to 1024. The current set of magnitude reducers is also eight which covers  10-3 to 10-24. The entire range is 10-24 to 1024. When this range is expressed using scientific notation there are 48 different and separate magnitudes to wrap one’s mind around. With engineering notation it is 16. What is incredibly useful when one uses engineering notation, is the seamless integration of linguistic expression and numerical expression.

Let me back up for a moment, and explain what I mean. When I was taking classes on circuit theory we used a number of components, the most prominent being resistors. Resistors are marked with colors, and the colors are coded for resistance values. I recall looking for a specific resistor I needed in my small stash and slowly working out the color sequence from a chart. My professor looked over my shoulder and said here, and picked one out immediately. I asked how he figured it out, and he said “I don’t, I just see the colors and I know.” It seemed impossible, but within two years—I could “see” the colors as numbers—and seldom needed a chart.

Within a couple of years I had a similar experience with engineering notation. When I would see 11.5 mm it would immediately be punched into my calculator as 11.5 x 10-3. If I saw 1.575 GHz it would go into my calculator as 1.575 x 109. The language designation and the numerical magnitude were indistinguishable. Without thought, my mind knew the equivalence between the prefixes and numbers. The prefixes milli, micro, nano, kilo, mega and giga required no thought, they were 10-3, 10-6, 10-9, 103, 106, 109. The engineering prefixes meld literacy and numeracy. Scientific notation has no such general linguistic equivalents. They are barren in providing an idea of their size using compact language. The use of scientific notation actually obscures numerical comparison. Here is an example from an article about Global Warming from New Scientist; it expresses four possible scenarios with respect to the amount of energy we use:

Let’s compare the scientific notation values from the article with engineering notation using Pat Naughtin’s Whole Number Rule:

Global Energy Use:

Scientific                     Engineering

1)   8 x 1020 joules            800 Exajoules
2)   1 x 1021 joules          1000 Exajoules
3)   8 x 1020 joules            800 Exajoules
4)   1.75 x 1021 joules     1750 Exajoules

Which column provides you with a better numerical “feeling,” as well as the ability to directly express the size of the number involved, as a number? If we lived in an effectively metric and numerate country, every pupil in grade school would have been taught, and know, that Exa is 1018. Despite living in non-metric America, I’m sure they’ve probably heard of Exabyte drives.

The use of engineering notation allows for a nice continuum of numerical expressions, which are immediately expressible in words alone—yet express an exact numerical magnitude. Scientific notation promotes unit proliferation. For many years, light was expressed in angstroms. One would have to recall that an angstrom is 10-10 meters. There is no metric prefix. There is no clue in the word angstrom as to what  its magnitude might be. In recent years the angstrom has been thankfully abandoned and light is generally expressed with nanometers, which I immediately know is 10-9 meters, just from the prefix nano. There are cases where values which are outside of the range of SI notation appear in engineering and scientific research work. Scientific notation alone must be used for this work.  But in all these cases it should remain without prefix designation as a value in scientific notation.  No googol for 10100 or logoog for 10-100 period. If they’re too big for SI one should leave them unnamed—until they are officially.

I came across the notes for a university course on the environment when I was searching to find out how many joules of energy are in a given quantity of gasoline. I came across this table which has the answer:

Energy Unit  ————————————————————–  Joules Equivalent (S.I.)

This is a clear example of an instructor believing that scientific notation allows for a meaningful comparison of values. Your friendly neighborhood Maven sees exactly the opposite. This person does not use any SI units in the “Energy Unit” column. There are gallons, pounds, tons, a barrel (which is in reality actually statistical), and a cubic foot. Not one metric unit appears on the left and only scientific notation is found on the right, with joules assumed for the column. I have sympathy for the instructor. This is a difficult set of numbers to express because of their large dynamic range, but metric prefixes can help considerably, and should have been employed. I will reorder the table, change it to metric in the left hand column, and compare a one kilogram mass of each substance:

Alternative Table — (click to enlarge)

I believe the use of increasing energy content is a good way to compare these energy sources. The new table shows that the energy density of the majority of the substances we use to supply energy have similar magnitudes. Five of the seven entries are from 20-53 megajoules. The large amount of energy in Uranium-235 is clearly evident when we keep the megajoule prefix, although it’s a very large number. The kilogram of AA batteries is only 0.211 megajoules. When we start with kilograms, the “conversion” of coal and uranium entries to megagram quantities (i.e. “metric tons”) may be done in one’s head. When pounds are used, one needs to multiply by 2000 to obtain a short ton and 2240 to convert to long tons. There is no designation within the table that explains which ton is used. Clearly in a course about environmental concerns, the most efficient and succinct way of presenting energy numbers is desired. The use of a mixture of units and scientific notation obscures the fact that most of the substances have similar energy content.

I see very poor expression of numbers and numerical data in popular science magazines, technical papers, and the worst, mass media publications. When I took English, I demonstrated a complete inability to internalize its grammatical intricacies. What I was told by the instructor was that the worst use of grammar could be found in newspapers and magazines. One could see the irony that these were people making a living using the English language, ostensibly professionals, who used poor grammar. When I first realized how badly numerical data was often presented in technical papers, I had a kinship with my English teacher that I had never experienced before. The lack of the metric system in the US, stunts the ability of professionals to express numbers in a cogent manner. The lack of the metric system in the US prevents teachers from instructing children at the earliest age possible about how to use metric prefixes, as they will not experience them in this society. The lack of the metric system in the US encourages the continued overuse of scientific notation which is an opaque way to express numbers. The lack of the metric system helps to keep us innumerate.

Updated 2014-05-30

Related essay:

The Expanding Universe

If you liked this essay and wish to support the work of The Metric Maven, please visit his Patreon Page and contribute. Also purchase his books about the metric system:

The first book is titled: Our Crumbling Invisible Infrastructure. It is a succinct set of essays  that explain why the absence of the metric system in the US is detrimental to our personal heath and our economy. These essays are separately available for free on my website,  but the book has them all in one place in print. The book may be purchased from Amazon here.


The second book is titled The Dimensions of the Cosmos. It takes the metric prefixes from yotta to Yocto and uses each metric prefix to describe a metric world. The book has a considerable number of color images to compliment the prose. It has been receiving good reviews. I think would be a great reference for US science teachers. It has a considerable number of scientific factoids and anecdotes that I believe would be of considerable educational use. It is available from Amazon here.


The third book is called Death By A Thousand Cuts, A Secret History of the Metric System in The United States. This monograph explains how we have been unable to legally deal with weights and measures in the United States from George Washington, to our current day. This book is also available on Amazon here.

Long Distance Voyager

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By The Metric Maven

Bulldog Edition

When it comes to distance, the larger metric prefixes are generally neglected. Astronomers feel justified in using Astronomical Units to describe distances within the solar system. When distances become large enough, the ubiquitous light-year is then employed with great relish and awe. One of the arguments offered for the absence of the larger metric prefixes in astronomy, is that the distances are just too large, and the metric system is overwhelmed. The distances are just too astronomical for the metric system to handle!—or even convey their vastness! Generally, this manner of argument masks a provincial desire by a specialty of engineering or science to have its “own” special measurements. It is also stated that people can only relate to Km and smaller metric measures because the other distances are outside of their everyday experience.

I have had the privilege of working with some incredibly talented engineers, including the Engineer, who designed the high gain dish antenna which resides on the front of the Voyager spacecraft. His name is Michel, and I once shared an office with him. The Voyager antenna would at one time have been within millimeters of Michel, it was then moved about 4000 Kilometers away from him so it could be launched into space on September 5, 1977 (1977-09-05). It ascended from our planet, which has a circumference of 40 Megameters. Michel’s antenna then passed the orbit of the moon which is about 384 Megameters from Earth. One could argue that the Voyager spacecraft was now in the realm of the solar system. At that point, its distance from the sun might be a more meaningful reference point to describe its distance from us. The Earth is approximately 150 Gigameters from the sun.

Gigameters is a useful length to describe the distances of our planets from the sun, as well as the current location of the Voyager spacecraft (2014-04-04). Michel’s antenna is part of the singular human-constructed object we call Voyager 1, and is further away from the Earth than any other space probe in history—and likely to remain so. Despite the fact that Voyager is now beyond our solar system, its distance is still readily describable in terms of Gigameters. Below is a table of planetary distances and Voyager 1 and 2:

I don’t recall any astronomers ever using Gigameters in school or on television, even though it is a convenient unit. Astronomers define their own “yardstick” which they call an astronomical unit. This astronomical unit is defined as the distance from the earth to the sun, therefore 1 AU = 150 Gigameters. I don’t see why modern astronomers, by which I mean astronomers who have been born after 1960, don’t use Gigameters instead. The prefix Giga was officially adopted in 1960. A Gigameter is certainly as convenient of a unit as an AU, and it’s tied to the meter, which is the universal measurement length used by science, and by 95% of the worlds population. When a person, even an American, sees the symbol Km, they see kilometers. The lack of use of the designation Gm for Gigameters by astronomers makes it unfamiliar and seemingly awkward. It is only the lack of general use which makes this so.

When Astronomers begin to describe distances outside of our solar system, they generally turn to another unit they coined which is unique to astronomers—the light-year. Wikipedia gives the definition of  a light-year as:

1 light-year     = 9460730472580800 metres (exactly)

This is where, if I were forced to write it in meters, I would use the three digit space convention to parse it. The three digit grouping allows a person to identify the appropriate metric prefixes with ease:

1 light-year     = 9 460 730 472 580 800 metres (exactly)

This expression allows one to immediately recognize the metric prefixes as one moves from right to left as: one, Kilo, Mega, Giga, Tera, Peta, and determine that 1 light-year = 9.461 Petameters (Pm). In my view the light-year is more of a “gee whiz” measurement metaphor than an actual length. It is like the kilowatt-hour. There is a metric prefix which is of sufficient magnitude to describe distances which have magnitudes in terms of light-years and it is Peta. The hypothetical Oort cloud is believed to be about 7.5 Petameters away, which when compared with stars, it not  far away.

Almost everyone knows that alpha-centari is the star closest to Earth (other than the sun). It is 4.366 light-years distant. This is 41.4 Petameters. So even when we are discussing the distances to stars, there is a sufficient metric prefix. The light year is not required, at least not after 1975, when Peta was adopted as a metric prefix. Here is a list of nearby stars, and a more distant one also in Petameters:

Constellation of Orion Betelgeuse is the upper left star which is about 6 Em from Earth. Rigel is on the lower right and about 8 Em from Earth — Click to enlarge                    (Wikimedia Commons)

Betelgeuse is a red giant which is in the upper left corner of the constellation Orion. On a clear night in Montana, when I lived far away from the city lights, I could clearly see its red color. Stars beyond Betelgeuse are at distances that may require the introduction of another metric prefix.  This would be the prefix Exa.  One could categorize stars which are “near” earth as those up to 1000 Pm and those beyond 1 Em (Exameter) as “far away” stars. This would make Alpha-Centari, Barnard’s Star and Sirius all nearby stars. Far away stars would include Betelgeuse (6.1 Em) and Rigel (7.7 Em). The farthest currently known star which is still inside of the Milky Way Galaxy is  UDF 2457. It is 558 Em distant.

When we approach the dimensions of the Milky Way Galaxy, we may want to describe the distances from the galactic center. The diameter of our galaxy dwarfs the distance from the sun to Betelgeuse. It is 1 000 000 Petameters across or, shifting metric prefixes, is approximately 1 Zettameter (Zm) in extent. From this information, we know that no star within our galaxy is more than a zettameter away.

The Andromeda Galaxy is 24 Zm from Earth and is visible with the unaided eye.                      (Wikimedia Commons)

Interestingly, we can directly see a distance which is much farther than the dimension our galaxy with the unaided eye. The nearest spiral galaxy is Andromeda, and it can be viewed with the “naked eye.” The Andromeda Galaxy is 2 540 000 light-years away or approximately 24 Zettameters (Zm). This is rather close. It is only 24 times the diameter of our galactic disk. The Andromeda galaxy is expected to collide with our Milky Way Galaxy in 3.75 billion years and form a large elliptical galaxy. Andromeda is not the nearest galaxy overall. The Sagittarius Dwarf Elliptical Galaxy is actually a satellite Galaxy of the Milky Way, that is, it orbits our galaxy. It is only 0.77 Zettameters from our galaxy (or 766 Exameters). This places it just a couple of hundred Exameters beyond the farthest known star within the Milky Way Galaxy.

Here is a short list of local group galaxies which are over one Zettameter away:

The Sombrero Galaxy is 265 Zm from Earth (Wikimedia Commons)

Sextans B is near the end of what is known as the local group of galaxies. The local group encompasses a diameter of about 100 Zettameters (Zm). Clearly there are lots of galaxies which are further away, so which one is the farthest known? The current candidate for the furthest galaxy is MACS0647-JD which is a whopping  125 825 Zettameters (Zm). We can see that we are well beyond a 1000 difference. Has the metric system let us down because of this astronomical distance? No, it has not, at least not since 1991. In 1991 both the Zetta prefix, and the Yotta prefix were added. The Yotta prefix allows us to write the distance to the farthest confirmed galaxy as 126 Yottameters (Ym). The end of the observable universe is approximately 435 Yottameters (Ym). The diameter of the universe is 870 Ym. Astronomical distances do not crush the metric system. There is no need for astronomers to resort to a light-year or AU or parsecs to describe astronomical dimensions. The metric system can in fact be useful to classify astronomical distances. For instance:

click to enlarge
Neil deGrasse Tyson — Host of Cosmos

The latest incarnation of Cosmos has been interesting to watch, but I can only wince when I hear Neal deGrasse Tyson use miles, billions of kilometers, astronomical units, and light-years to describe the cosmos. This archaic measurement usage seems like a lack of respect for the metric system on the part of the Cosmos producers. It is 34 years after the original series was aired. When the original Cosmos aired, the Zetta and Yotta prefixes had not been added to SI. One could see why metric might not have been invoked. Indeed, SI was not large enough to encompass the universe, but like the universe, it expanded. Unfortunately, the root cause for the lack of the metric system in Cosmos could possibly have an even less desirable origin—it could just be unawareness. It is even possible it is the product of a culturally encouraged unfamiliarity. This culturally sanctioned ignorance, if that is the root source, was fortified at the same time as the first airing of Cosmos in 1980. It was in that year that Ronald Reagan quashed any possibility of measurement reform in the US, by disbanding the metric board. This disbanding was an attack on modernity and efficiency, mantled in a red herring of cost savings. It was a narcotic of intellectual flattery perpetrated by a cultural embargo, which has numbed the minds of the American public to the spectrum of metric prefixes, and in turn, it has cost lives. If there is another edition of Cosmos 34 years from now, I can only hope, that by then, it uses the metric system.

Related essay: Neil deGrasse Tyson and The Metric System

This essay was edited on 2016-10-15 to conform with The Elements of Bile.

If you liked this essay and wish to support the work of The Metric Maven, please visit his Patreon Page and contribute. Also purchase his books about the metric system:

The first book is titled: Our Crumbling Invisible Infrastructure. It is a succinct set of essays  that explain why the absence of the metric system in the US is detrimental to our personal heath and our economy. These essays are separately available for free on my website,  but the book has them all in one place in print. The book may be purchased from Amazon here.


The second book is titled The Dimensions of the Cosmos. It takes the metric prefixes from yotta to Yocto and uses each metric prefix to describe a metric world. The book has a considerable number of color images to compliment the prose. It has been receiving good reviews. I think would be a great reference for US science teachers. It has a considerable number of scientific factoids and anecdotes that I believe would be of considerable educational use. It is available from Amazon here.


The third book is called Death By A Thousand Cuts, A Secret History of the Metric System in The United States. This monograph explains how we have been unable to legally deal with weights and measures in the United States from George Washington, to our current day. This book is also available on Amazon here.