In the first half of August 2023, there were reports about NASA accidentally losing contact with the Voyager 2 spacecraft after sending the wrong command and later reports about regaining contact a few days later. Distances of spacecraft from Earth were expressed in billions of kilometres (as well as billions of miles). One thing that NASA and the media ignored is that the common prefixes of the metric system for the extremely large and the extremely small make the use of astronomical numbers unnecessary unlike the imperial system. This is one big advantage that the metric system has over the imperial system.
In common usage, no prefix larger than kilo is used for the metric unit of length. So, when there is a need to express enormous distances, we end up seeing distances expressed in thousands, millions and billions of kilometres. Recently, NASA and the general media reported that Voyager 2 is more than 19.9 billion km from Earth and that Voyager 1 is almost 24 billion km from Earth.
This is unlike other units where the kilo prefix is commonly used. Many would defend this practice by arguing that larger prefixes used with metres are unfamiliar to the generic public. It ignores the fact that familiarity comes with usage and people soon get used to seeing larger prefixes used in specific contexts.
For example, I remember the old days of computing when kilobytes were enough to express storage and file sizes and kilohertz was enough to express computer processor speeds. The figures for both in the old days were well under a thousand. As computers became more powerful, we did not talk about thousands or millions of kilobytes and kilohertz but used the larger metric prefixes, so we got used to megabytes and megahertz, and later, gigabytes and gigahertz. These larger prefixes were not used until we needed them.
When we talk about power consumption, we typically use watts for bulbs and kilowatts on household energy bills. We would use megawatts for a small power station’s output and gigawatts for large power stations and national power output. When discussing global power consumption, we would use terawatts.
When we talk about body weight or gym equipment in metric units, we use kilograms. For heavier weights such as the weights of large vehicles, we use tonnes rather than thousands of kilograms. One tonne is exactly 1000 kg. Kilotonnes and megatonnes are used to express amounts of carbon emissions for areas and countries respectively. We do not normally express such figures in millions and billions of kilograms.
So why are we so reluctant to use any prefix larger than kilo for the metric unit of length? Is it because the kilometre is seen as the metric equivalent of the mile? Is it because we are used to seeing extremely long distances expressed in millions and billions of miles?
Here is a table of some larger quantities that can be used to express distances in metric units:
| Metric Unit | Metric Symbol | No. of Metres | No. of Kilometres |
|---|---|---|---|
| megametre | Mm | million (106) | thousand (103) |
| gigametre | Gm | billion (109) | million (106) |
| terametre | Tm | trillion (1012) | billion (109) |
| petametre | Pm | quadrillion (1015) | trillion (1012) |
Existing prefixes for the extremes at both ends of the scale remove the need to use astronomical numbers with metric units. When the most appropriate prefix is used, the use of extremely large numbers can be avoided. The distances of Voyager 1 and Voyager 2 from Earth could be expressed as 24 terametres and 19.9 terametres respectively. The wide range of prefixes provides the metric system with the capability to measure the extremely large (such as the longest distances and biggest objects in the universe) and extremely small (such as the smallest particles in the universe).
By contrast, the range of the imperial system is a lot smaller at both ends of the scale. The longest imperial unit of length is the league, equivalent to three miles, but that is no longer an official unit in any nation and is seldom used. So, the second longest imperial unit of length is used, which is the mile. This is used for measuring all long distances, no matter how long. For distances across the universe, the use of extremely large numbers is inevitable in the imperial system. In the metric system, there are larger units than the kilometre that can be used to avoid the use of enormous numbers. This is the whole point of metric prefixes – it enables us to avoid the use of enormous numbers.
Further reading:
- https://en.wikipedia.org/wiki/Imperial_units
- https://ukma.org.uk/what-is-metric/definitions/prefixes/
- https://www.jpl.nasa.gov/news/nasa-mission-update-voyager-2-communications-pause
- https://www.itv.com/news/2023-08-01/nasa-loses-contact-with-voyager-2-after-sending-wrong-command
- https://www.bbc.com/news/world-66371569.amp (“Voyager 2: Nasa picks up ‘heartbeat’ signal after sending wrong command” by Andre Rhoden-Paul, 1 Aug 2023)
- https://edition.cnn.com/2023/08/01/world/voyager-2-communication-blackout-scn/index.html
- https://metro.co.uk/2023/08/04/voyager-2-back-in-contact-with-nasa-after-stint-flying-blind-19276945/?ico=tag-post-strip_item_1_news
- https://www.itv.com/news/2023-08-01/nasa-loses-contact-with-voyager-2-after-sending-wrong-command
- https://www.nasa.gov/feature/jpl/nasa-mission-update-voyager-2-communications-pause
Metric Views 
I agree with your central point. The use of “large counting words” with SI units should be avoided and replaced by suitable prefixes. Another line of argument is “what is a billion?” Since the UK adopted the short scale 10^9 billion in 1973, English seems to have a pretty common short scale agreement, but many other languages are still long scale and billion is 10^12, so “large counting words” are imprecise across language, while SI prefixes are well-defined.
I would note (unfortunately) that kilotonnes and megatonnes may be used for sciencey things like CO2 emissions, the USDA widely publishes grain export figures in thousands and millions of metric tons. Since 1 t = 10^6 g, it might be better to use megagram, and suitable larger prefixes with the gram rather than the tonne or metric ton. 1000 t = 1Gg, 1 000 000 t = 1 Tg.
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Talking about incorrectly using metric units of length, the only thing I can gather is that people are thinking of the different prefixes as separate units instead of prefixes to the base unit.
This seems to me a by-product of incorrect education on how to properly use the extremely simple SI metric system.
For some reason people think of the prefixes along with the base unit as separate units instead of just multipliers or sub-multipliers of the base unit.
Get rid of A.U., 1 A.U. ~= 1.50 gigameters
Get rid of Light Years, 1 LY ~= 9.46 petameters
Get rid of parsecs, 1 parsec ~= 30.856 petameters
S.I. Metric is so simple, there is only one unit for length, it is “meters”, but you also need to properly use the prefixes.
With respect to the mass unit, in my opinion, the best thing to do is to simplify and make use of the SI Metric system as it was and is intended to be used is to rename the badly named “kilogram” unit.
I suggest “klug” to keep the the symbol the same.
The SI rules forbid the use of ‘kilo kilogram’, therefore people have to use the gram or the tonne and things get wierd and you can’t use it as it was intended and people get confused.
With “klug” or any other name without “kilo” in the name:
1000 milliklugs (1000 grams) = 1 klug (base unit of mass)
1000 klugs = 1 kiloklug
…
The same concept: The concept of “volume”, the “cubic meter” is completely accurate but more of a description than a name and that causes the base unit to be hard to use and say and people result to using the “liter” and then incorrectly think it is the unit for volume.
If we could give a name (rather than more of a description) to the concept of volume which is a derived unit from linear length, then people could easily use it and not think that “liter” is the derived unit for volume.
There is already a name for it: “stere” ( See https://en.wikipedia.org/wiki/Stere URL ), let’s use that.
1 mL = 1 microstere (µst)
1 L = 1 millistere (mst)
1 stere (st) = 1000 millistere (mst)
I am constantly finding web sites (even educational ones) which claim that the gram and the liter are the units for mass and volume when 1 cubic meter and 1 kilogram are the correct units.
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I’ve been saying this for years, that SI units are not taught correctly in any school in the world. Basically what is taught is old cgs. where the prefix range is limited and counting words are mixed with prefixes.
SI is both taught an advertised as a sysmtem based on 10s where one “unit” is converted to the next “unit” by moving the decimal point. This simple is the wrong analogy.
In SI, there is only one unit for each item measured, whether it be mass, length, time, energy, force, etc, and the prefixes only add a scaling factor not create a new unit. Each unit relates to each other in a 1:1 ratio via a mathematical formula. For example with F = ma (Force equals mass time acceleration, the unit newton for force is created by multiplying the mass in kilograms with the acceleration in metres per second squared. Thus in symbols: 1 N = 1 kg.m/s^2.
SI is not about moving decimal points but about having a consistent and coherent set of units that harmonise with nature and being able scale the result within a range of 1 to 1000 with an appropriate prefix.
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I agree with John Steele about billions. I was originally taught that a billion was a million squared, and a trillion was a million cubed, and so on. The short scale form lacks logic. It does not translate well across languates, for example the Germans call 10^9 a milliard. Why could we not have adopted that word instead. Also, using the short scale million seems to reduce the scale of the whole number. Partially to avoid ambiguity, I avoid using billions and instead use thousands of millions. A figure like 24 000 million appears much larger than 24 billion and makes comparison easier.
The more-extreme prefices, e.g. tera, atto, are more difficult to memorise. For involved mathematics, scientific notation (exponent power of 10) is more useful for handling very large or very small quantities, though of course this would be cumbersome for trading figures.
Why did the media, politicians, financial organizations, etc, choose to adopt the short scale billion? My guess is that they don’t know themselves.
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Metricmac,
You will note that the names of the numbers are derived from the long scale notation. Bi- as in bi-million or billion means two and it is the number you multiply 6 by to get the number of zeros. Since 6 x 2 = 12, a billion would be a 1 followed by 12 zeros. Tri means three so trillion means 6 x 3 zeros or 18 zeros. An octillion would be would be a 1 followed by 48 zeros, since oct means 8 and 8 x 6 = 48.
Since there is a big gap between each number, the gap is filled in by adding the suffix -iard, which adds an additional 3 zeros. So, between a million and a billion is a milliard and since a million is one followed by 6 zeros, a milliard is a 1 followed by 9 zeros. A billiard is a billion plus 3 zeros or a 1 followed by 15 zeros. An octiliard is a 1 followed by 48 + 3 zeros or 51 zeros.
Very simple.
With the short scale, it is almost impossible to guess what a number name means and as a result most short scale lovers can’t count past a billion. Some may know what a trillion is and even fewer what a quadrillion is in short scale. But, I sure only a handful can even guess what follows quadrillion.
The short scale is most likely the main reason short scale users are highly innumerate.
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