Converting between metric and inferial

Many times one needs to convert only approximately between metric and inferial* values.

Converting dimensions expressed in mm to inches in your head is easy. You need to divide by 25.4 which is the same as multiplying by 0.03937 which is very close to 0.04 which is 4/100. Simply double the metric dimension twice and move the decimal two places to the left. The error associated with this approach is only 1.6%.

Example: 37 mm -> 74 -> 148 -> 1.48 in (correct value = 1.4567 in}

Converting an inferial fraction expressed as a ratio to mm is also done by dividing by 25.4. Now 25.4 is very close to 256/10 and dividing by this number is the same as multiplying by its inverse 10/256. Since 256 is a power of two and the denominator of any inch fraction is also a power of two, this suggests the following procedure:

Keep doubling numerator and denominator until the denominator is 256. Then the numerator divided by ten is the equivalent in mm with an error of only 0.78%

Example: 13/64 in = 26/128 = 52/256 -> 52/10 -> 5.2 mm (correct value = 5.159375 mm)

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* I live in the USA, the only industrial nation on earth that hasn't adopted the metric system. Usonians will tell you that we use the Imperial system but that isn't strictly true. True, we obtained most of our system from Britain but we further botched and confused it into the mess now known as American Customary Units. That's a mouthful to say or write and few will know what you're talking about.

I decided to make up my own designation for a system that has seven different units all called "barrel". My "inferial" is a portmanteau of "inferior/infuriating" and "Imperial".

Thanks for this post and the new word "inferial" that you have coined. I notice that in more than 5 months since this was posted
that nobody has bothered to reply. I can only conclude that people living where you live have no idea what you are talking about and that people living in the rest of the world no longer have a use for ‘inferial‘ units. Almost 49 years since we were metricated down here in N.Z.
There must have been no love lost between post civil war Americans and their former colonial rulers. It seems everything had to be changed, gallons, pints, quarts, driving on the right instead of the left, 110 volts not 230, 60Hz not 50 Hz, and I believe that even the rifleing twist in gun barrels twists in opposite directions, (due to gyroscopic precession and earth rotation this makes US weapons less accurate, in the northern hemisphere and they must know this but will not change.) There must be countless other examples of this stupidity. Having said all of the above, I don‘t think that America will go Metric in the foreseeable future. It would be like asking the American people to change their flag, (apart from adding a star or two), it is not going to happen, and rightly so.

Thanks for the response.

You're absolutely correct about Americans' stupidity in absorbing English Imperial units. While the metric system had not been created at the time we broke from the English, we at least had the opportunity to eliminate some of the obvious idiocies in the English system. While we adopted decimal currency and abandoned the stone as a measure of weight, we hung on to most of the units of convenience the English have the nerve to call a "system".

It's impossible to have an intelligent discussion of the problem with most Americans. The technical ignorance of the general public is appalling. Many of them believe the metric system is a European attempt to subvert their liberty. Another segment, which includes many machinists, argues that the metric system isn't as "accurate" as the inferial system. The fact that the notion of measurement system "accuracy" is a meaningless concept is completely lost on them. Many of the other counter-metric arguments are equally nonsensical and absurd. Just about all of them don't know what a measurement "system" is. Of course, it doesn't help that the average American is completely dumbfounded by even the simplest mathematics.

I often joke that, if the Americans adopted the metric system, they would have two measurement systems they couldn't understand. Sadly, my joke becomes truer every day.

Marv,
For some of us measurements just become numbers that become second nature. I have a PhD in geophysics where all my education and research was in calculating formulas with the metric system and I got very use to understanding the numbers and order of magnitudes to know if the answers even made sense. I then work 25 years in oil and gas exploration for an oil company where we used both metric and imperial measures, and a mixture of the two systems in the same calculations (dimensional analysis became very important). After a while everything becomes second nature and in the end just some numbers that represent the physical world. Understanding the physics represented by the numbers was more important to me than the system of measurement but I can see your frustration.
Paul