Rounding off has ups and downs

20 December 1998

Financial and top managerial people may at last be catching up with engineers and scientists in arithmetic. The European Commission has recently been thinking about the introduction of a statutory procedure for the rounding of the figures involved when converting between different currencies: this could matter particularly for transactions involving complex contracts.

According to Professor Julian Hunt, writing in Mathematics Today, truncation and rounding errors often occur in the calculation of performance and financial indicators in many organizations, as well as in scientific and engineering calculations.

In his discussion of the rounding and other approximations used for measurements, records and targets, Hunt mentions three different ways of rounding up or down when a figure lies midway between the two choices. You can take the even values, rounding for instance both 49.5 and 50.5 to 50 and turning 'quarters' into 0.2 and 0.8. Or you can, in the jargon, 'throw to the odd', rounding 49.5 and 50.5 to 49 and 51 respectively and turning quarters into 0.3 and 0.7. Or you can (as probably most engineers do) always round up, say from 49.5 and 50.5 to 50 and 51.

Hunt tells us that all three rules are used according to circumstance by actuaries but that weather forecasters tend to throw their temperature measurements to the odd. He suggests reasons of convenience or bias for various people's selections but finds them all rather arbitrary.

His conclusion involves a piece of advice that seems surprisingly homely in a high-powered mathematician's thesis for what are, presumably, our most numerate professions: 'If the even/odd rounding principles are impractical the only safe way to ensure reasonable accuracy is to delay rounding until the final stage of the calculation . . . Therefore, when using calculators and computers, it is essential to use numerical values with more significant figures than are required for the calculation . . . Ideally, for important and sensitive calculations one should check that the size of the calculation is such that any arbitrary or unbalanced rounding does not affect the final answer.' The same principle used to be part of the teaching of decimal fractions to schoolchildren long before computers and pocket calculators were invented!

Appropriately, therefore, Hunt's article in Mathematics Today opens with the assertion that there is nothing new about quantitative assessment of organizational performance. The first known management consultant, says Hunt, was Jethro, who appears in the biblical Book of Exodus as the man who formulated the numerical foundation of the ancient Israelites' reporting system (teams of thousands, hundreds, fifties and tens).

Jethro may have gone one better than presentday gurus, however. Hunt observes drily that the Hebrew patriarch of the consultant tribe 'properly ensured afterwards' that his system worked.

“All the choices are rather arbitrary”

These may virtuously be nuked

The International Atomic Energy Agency is publicly well pleased with itself for having helped to wipe out the tsetse fly in Zanzibar.

The fly is a notorious vector of disease in sub-Saharan Africa, where it spreads trypanosomosis among livestock and sleeping sickness among people. Zanzibar has apparently been liberated from tsetsean devastation of its herds, a relief achieved by radiatively sterilizing large numbers of male flies and letting loose weekly waves of them on the females.

The Agency says that 36 sub-Saharan countries, one of which is Tanzania, suffer tsetse infestation. Zanzibar island, a part of Tanzania, has been the site of a ten-year internationally sponsored pilot project in which culminating application of the now well established 'sterile insect technique' seems to have delivered total victory. The ultimate aim is the eradication of the fly from 25 000 km2 of the Rift Valley in mainland Africa.

The IAEA press release does not report that there has been any popular resistance to the campaign so I dare surmise that nuclear abolitionists and biodiversity conservationists alike, on this occasion, forbore. Farmers, profiting from healthier cattle, should be grateful. They and other Africans may yet go on to benefit from macro as well as micro manifestations of nuclear energy.

If they are granted that precious forbearance.


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