Sorry: We are unable to offer 50% off as we do not put 50% on

This is a cute sign, but does the shop owner really understand percentages?

Whenever I visit my family in Plymouth, I walk past a shop window with the above sign on it. The sign has been there for years apparently. It's sort of amusing, but at the same time I can't help wondering whether the shop owner understands percentages. According to the normal rules of percentages, you would have to add 100% to be able to take 50% off. However, the statement "We cannot take 50% off as we do not put 100% on", although accurate, loses its poetry. So what could the shop owner have said that was both accurate and as cute as the original sign? I can't think of anything, but it doesn't excuse muddled thinking.

The use of percentages is often garbled in society. In writing about changes in numerical quantities journalists (who are usually the biggest culprits) have two choices that are used to create variety and style in their articles. The first is to quote a percentage increase ("The economy has expanded by 4.8% in the period 2010-2013") or a factor increase ("The number of people in the world has increased by a factor of 4.6 since 1900"). There is no harm in this if the numbers are accurate. Difficulties arise when a factor increase is translated into a percentage increase. For some reason or other a large percentage is somehow seen as emphasising more the item being described. For example, sometimes that factor of 4.6 increase will mysteriously convert to a "460%" increase, whereas of course it is actually a 360% increase. Therefore, whenever I see large percentage increases (above a few hundred) written by non-technical people, I nearly always wonder whether the number is correct or not. It is not as if percentages are difficult to understand: most young children are taught them at school, so why have most adults forgotten the rules despite their frequent use in society? Perhaps it is the misuse which is eroding understanding.

Whenever I see large percentages, I am now on the lookout for the worst abuses For example a 5% increase can't be confused with a 105% increase. So where does the cross-over occur? Is it around a factor of 2 increase which mysteriously becomes a 200% increase? I suspect so, but obtaining the raw data is not easy and many journalists apparently still remember simple arithmetic and get their percentages correct anyway. Unfortunately, enough writers seem not to get the numbers right.

I am reminded of the situation in Britain regarding temperature, which I mentioned in my book Measuring the World: Making complicated problems simpler by really going metric. If you carry out a survey of people at various times in the year, and ask them what the temperature is without specifying the units, then they will not be consistent. A cold day in winter is usually indicated in Celsius as the temperatures are close to, or even below the emotive 0 degree value. On a warm day, the temperature flips to Fahrenheit. So what is the temperature at which people unwittingly flip from Celsius to Fahrenheit? Apparently it's about 10 C!

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