Dear Editor,
Mr. Sean Brignandan’s reasoning on Imperial and metric measures used on a weighing scale is extremely flawed and abysmally uninformed.
He claims that if 1 pound (lb) is measured on an Imperial scale the margin of error is 1 ounce (oz). This, however, is only true when the smallest graduation on the scale is 1 oz; such scales are not manufactured. The familiar red Imperial scale used in many businesses has a better accuracy than Mr. Brignandan’s Toyland scale. Because its 1 lb (16 oz) poise serrated sliding arm has 64 graduations, the smallest graduation is 0.25 oz, giving the Imperial scale an absolute margin of error of +/- 0.25 oz. Therefore, the relative margin of error associated with the measurement of 1 lb is +/- 1/64 lb or 1.56 %. The +/- sign indicates that the error can go either way, that is, the business could be overcharging or undercharging by 1.56 % on a 1 lb measure.
With a properly maintained scale and using the correct procedure, the small overcharging/undercharging becomes a random 50-50 event uncontrolled by the seller or the buyer. The attempts of the buyer and the seller to gain control over the measuring process can be amusing and enlightening to observe.
Buyer: “Mister, let the scale pan go down hard. I want to hear it.”
Seller: Lady, it only got to balance, not go down hard.”
After some good-natured (?) haggling, a compromise is soon reached and both parties leave the transaction satisfied.
It is important to note that as the quantity measured increases, the size of the margin of error relative to the quantity decreases. Thus, if one measures 2 lbs, the absolute error remains +/- 0.25 oz, but the relative error drops to +/- 1/128 lb or 0.78 %, so that the overcharging /undercharging falls to +/- 0.78 %. So it makes sense to measure up to the maximum allowable pounds on the scale as it reduces the relative error and also the overcharging/undercharging percentage. Motto for the buyer: Buy in bulk. Motto for the seller: Work out your own salvation
Now for the metric scale and Mr. Brignandan’s grossest misinformation. He claims that if 1 kilogram (kg) is measured on a metric scale the margin of error is 1 gram (g). This can only be true if the smallest graduation on the scale is 1 g. On the red metric scale, approved by the GNBS, the 0.5 kg (500 g) poise sliding arm has 50 graduations. The smallest graduation is therefore 10 g, giving an absolute margin of error +/- 10 g. To achieve an accuracy of +/- 1 g, the sliding arm would have to be 10 times longer (over 1 metre) or additional sliding arms with finer graduation would have to be added. In either case, the scale would be too delicate and bulky (not to mention prohibitively expensive) to be lugged around easily by market vendors and shop-keepers.
With the realistic +/- 10 g absolute error, a 1 kg mass will have a relative error of 1/100 kg or 1 %. But hold. If I had previously needed 1 lb (454 g) of meat, why should I now purchase 1 kg (2.2 lbs)? The metric scale cannot measure 454 g; it gives 450 g, with an associated relative error of 1/45 kg or 2.2 %. As well as losing 4 g, I would be subjected to +/- 2.2 % overcharging/undercharging. Hence, to measure 1 lb (approx. 450 g), the relative error on the Imperial scale is smaller at 1.56 % than the metric scale 2.2 % relative error. The Imperial scale, with an absolute error 0.25 oz (7.1 g), is therefore more accurate than the metric scale, with an absolute error of 10 g (0.35 oz). For the metric scale to be more accurate than the Imperial scale, the length of the 500 g sliding arm would have to be doubled to accommodate 100 graduations so as to give a 5 g absolute margin of error. But is this practicable? Nevertheless, we should be thankful that the correction of Mr. Brignandan’s error has led us to some truth. Finally, the margin of error and the consequential overcharging/undercharging do not depend on the measurement system used, but on the quality and design of the measuring instrument (and also the integrity of the seller). The GNBS should not pressure buyers and sellers to go metric. Educate; don’t frustrate. Give people time to adjust. As always, focus on the children and young teachers in school; we older folks are too bent in our Imperial (and more accurate?) ways.
Yours faithfully,
M. Xiu Quan-Balgobind-Hackett
