The conflict between measurement choice and accuracy

When the Government launched its “Choice on units of measurement: markings and sales” consultation, it stated that it is committed to reviewing the current law to identify how more choice can be given to businesses and consumers over the units of measurement they use for trade, while ensuring that measurement information remains accurate. These two objectives are in direct conflict. If you want to know how they conflict, read on.

Where there is a choice of measurement units, there are problems with rounding errors. This leads to ambiguity about which unit is the primary unit and which one is the supplementary unit.

For example, let’s suppose we see Cox and Bramley apples on sale in a supermarket. If we only used imperial units and both varieties are priced at 45p/lb, there is no doubt that they are the same price. If we only used metric units and we see Cox apples for 99p/kg and Bramley apples for £1/kg, we can clearly see that the Cox apples are cheaper. If we use dual units and we see Cox apples priced at 45p/lb, 99p/kg and we see Bramley apples priced at 45p/lb, £1/kg, it is unclear whether they are the same price or not. When we use dual units, we also have the same problem when one is priced only in pounds and other is priced only in kilograms. When one variety costs 45p/lb (with no metric equivalent) and the other costs 99p/kg or £1/kg (with no imperial equivalent), it is unclear which costs more or if they are the same price. We still have the same problem because of rounding errors. In this case, there is more choice but accuracy is compromised.

We will also face the same problem when some fridges’ capacity is expressed in litres and others are expressed in cubic feet. Where there is a discrepancy between two incompatible units, this is likely to be caused by rounding errors in unit conversions. Where dual units are used, it may be unclear to consumers which unit is exact and which one is approximate.

During the pandemic, the Government social-distancing guideline was that we should keep a distance of 2 metres from others. When expressed only in metres, just one unit is used, and it is 100% accurate. Many social distancing signs gave a conversion of 6 feet. Most included metres but a few only used feet. The conversion error was almost 10%. Six feet is exactly 1.8288 metres. This is a classic example of a trade-off between choice in measurement units and accuracy.

It is unclear how the Government intends to increase choice over the units of measurement while ensuring that measurement information remains accurate. Using multiple systems for measurement compromises accuracy due to rounding errors and ambiguity.

11 thoughts on “The conflict between measurement choice and accuracy”

  1. Just imagine if traders were allowed to continue to list prices for their goods or wares only in pounds/shilling/pence even after the decimal currency was introduced and people had to convert in their heads (well before smart phones and a possible conversion app). Who would think such a daft idea made any sense.

    Alas, when it comes to metric and Imperial, no such analogy seems to take hold!

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  2. One contributor here (John-xx I think), gave a real life good bad example of this when trying to make panels for an American aircraft wing specified in inches using metric machinery.
    The accumulative conversion errors in a row of rivet holes made automated drilling impossible, with corrections being made every 5 holes or some such. An expensive loss making contract I guess.

    It seems to me no where near enough is said, (media in particular) about this perpetual time wasting, loss making, infuriating muddle of mixed units.
    Even now we have to question “.. is this really a metric part, or is it just a ‘descriptor’ figure?” “Will these two parts really fit together, or are they different specs?” Bad enough in a domestic DIY household, not sorry I got out of industry where this was a perpetual issue. The daily cost to industry must be phenomenal.

    The cost of NOT going fully SI, of NOT fully educating our workforce in SI, and the cost of every second of every day perpetual conversions, errors, wasted ink, wasted paper space, it all adds up.

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  3. BrianAC,

    This is a big problem in the US. It is often assumed that American products are FFU, but most are not. They depend heavily on imported technology that is often hidden metric. If their internal operations are FFU, then they have to go to the added expense of making the parts fit. The result is a hybrid. Almost everything still made in the US is a hybrid with some exceptions.

    Many large multinational industries are as SI or metric as they can be such as automotive and heavy machinery. Their products tend to be designed, engineered, manufactured and serviced in SI, but that is often hidden from the general public. Aerospace tends to be stuck in the FFU past and as a result pays the price. They can’t share technology with other industries that are fully metric and if they want to sub-contract some production they almost can’t find enough suppliers that can do it accurately and profitable using FFU. As noted, the supplier has to convert the inch dimensions to SI and then round the numbers to within limits they can produce with, resulting in round-off errors.

    An example of metric made products hidden behind an inch descriptor is panel wood. 4 foot by 8 foot is really 1220 mm x 2240 mm. It may only be a slight increase but the extra 1 x 2 mm does add up in the same way the rivet spacing in your example does.

    The Luddites think they have sufficient power and influence to force a reversion to FFU, even in industry, at least the American ones do. Fact is, they don’t and they are slowly pushing their companies towards bankruptcy. Many dinosaur companies are already gone forever. I’m sure the former English government officials promising a return to FFU thought it would be easy to force industry back to the 19-th century and everyone would happily comply. I’m sure that those who run companies and had sleepless nights over the possibility of this nightmare coming to fruit worked their magic behind the scenes to prevent it. At the expense of removing government officials insisting on a reversal.

    Time is on the side of the metric system. The cost to those that insist on resisting continues to grow at their expense.

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  4. When it comes to accuracy or loss of it, this happens quite frequently especially in dual labeled products. In the US, most products sold in stores are imported from companies outside the country and are produced in rounded metric units. Even though US laws require dual labeling on most products and the choice of what units are primary is up to the seller, more often than not the products are sold with FFU being the primary units.

    So when the rounded metric value is converted to an FFU value (usually millimetres to inches) the calculated result is a highly decimalised number. The final number chosen is not just a simple rounding or truncation of extra digits, but an aggressive rounding to a whole a common fractional part.

    For example, a piece of floor tile that is exactly 200 mm square would be converted to 7.874 inches then would be rounded to 8 inches and sold as an 8 inch square tile. The metric that would be marked in parenthesis would not be the original 200 mm or 20 cm, but 203.2 mm or 20.3 cm. Consumer products are often labeled in centimetres to one decimal place instead of to millimetres with no decimal parts.

    So, in this example, both the FFU and metric dimensions are wrong. Accuracy is compromised via the deliberate attempt to hide the real metric value and replace it with a fake rounded FFU value and a metric value that is 3 mm larger than what is actual. Now factor this process in to every product sold.

    No one complains because they don’t bother to verify and if someone were to complain the companies would argue that the dimensions are either just trade descriptors or approximations. As was done with TV screen sizes over 10 years ago when they were sued for overstating the inches in this very manner.

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  5. I work as a technical writer for a very large tech company that is international and builds data centers and installs equipment in colocations all over the world. Our engineering data is a huge mish-mash of Imperial and metric because the headquarters are in Silicon Valley and the majority of workers reside in the USA. Most units are sadly Imperial for lengths but temperatures are degrees Celsius, air movement is cubic feet per minute, rack placement is in millimeters from a fixed point on the data center floor, etc. etc. Crazy!!!

    I have tried to add reasonable metric equivalents in all my documentation for the Imperial I do get from engineering, which employees in the other countries outside the USA greatly appreciate. However, here in the USA I have gotten some push back against doing even that minimal stuff. Unbelievable. We would all be so much better off to standardize 100% on the SI.

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  6. In 1215 the Barons forced King John to sign the Magna Carta. One of the clauses stated that there should be one system of units “throughout the realm”. This was not the case in France where the king had a set of units of measure that applied to the king’s taxes, the duke had his own set, the local lord another set and the local merchant his own set. It is said that in 1788 a quarter of a million different units of measure, many with the same name, existed in France. You can be sure that the peasants did not benefit from this multitude of units of measure.

    When the French Revolution broke out, the citizens (as they were), had lists of demands for reform. One of the items on these lists was reform of the system of weights and measures. The revolutionaries decided to use state-of-the-art thinking and thus the metric system was born. Maybe those who are clamouring for a return to the imperial system should remember this – allowing traders to dictate the units of measure that should be used on their stalls is seldom in the interests of the customer rather than the trader. BTW, the so-called “metric martyrs” are traders, not ordinary customers.

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  7. Ezra Steinberg wrote:

    I have tried to add reasonable metric equivalents in all my documentation for the Imperial I do get from engineering, which employees in the other countries outside the USA greatly appreciate. However, here in the USA I have gotten some push back against doing even that minimal stuff.

    I’d be curious to know from whom you are getting the push-back from and what reason is given for not wanting metric equivalents added. Is someone thinking that by not having metric present it will force a foreign metric user to have to learn FFU and become endeared to it?

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  8. The timber merchants in the UK will be dead against returning to imperial units because it will show up a “dirty practise” that they have ben employing for years. Before the UK joined the EEC, the dimensions of planned timber was the dimensions of the rough wood before planning. There was a maximum amount that could be planned off. Thus 2×4 planned timer was actually 1_7/8 x 3_3/4 – the user had lost 1/16 inch or 1/8 inch due to planning (and the merchant kept the shavings for making chipboard). Unless the EEC/EYU rules requiring the stated dimensions to be the actual dimensions were revoked, then the merchants could no longer call that timer 2×4. Revoking those rules would involve the UK n longer observing OIML recommendations which in itself would cause many problems.

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  9. Martin,

    So why couldn’t you start out with a rough piece being 52 mm x 102 mm and after planning make it 50 x 100 mm? If you start with 50 mm x 100 mm and plane off just 2 mm on a side you end up with 48 mm x 98 mm.

    In the US, the old 2 x 4 ends up after planning to be 40 mm x 90 mm, which means they are either planning off a lot more than in the UK or they start off with a smaller size and 2 x 4 is just a trade descriptor with no connection to a real dimension.

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  10. @Daniel
    My sense is that some folks here in the USA are so America-centric that they just don’t see the need to look past what “works” for us here in the USA. And it doesn’t help that the majority of our employees reside in the USA even though many have come here from other countries.

    I should add that many employees at my company who work in the USA are OK with adding metric but I am pretty much of an outlier trying to always add metric and advocate for metric. If I add a comment to a document or slide deck suggesting the addition of metric it is a totally up to chance if the comment gets accepted or not.

    Basically, there is no real push or active acceptance of metric in my company, alas. Would that it were different. But I will keep trying.

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  11. Ezra,

    It would seem logical if those employees that come from outside would push for things that would make the product more user friendly to those in their home country. Obviously they are so afraid of making waves, they refuse to get involved. But the push for metric really needs to come from them. They have to grow some cojones and make it an issue. But, I’m afraid they won’t unless they are coaxed.

    All I can say is keep pushing and never give up.

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