Harry Shannon
I was travelling on Via Rail, Canada’s national train system. The carriage was fairly new and a small screen showed the train’s speed. The highest I saw was 161 km/h. I wanted to know whether or not this was just over 100 mph. So I used a calculator app on my iPad to check. I downloaded it a while ago and don’t remember any details.
There are 2.54 cm in an inch. My first step was to see how many inches there are in 161 km.
161 km = 161,000 cm, so I needed to divide that by 2.54.
Here’s what happened:
But then I looked more carefully at the result (the long string of numbers). It didn’t seem right: 161/2 is about 80, while 161/3 is about 50. Since 2.54 is between 2 and 3, the result should have been between about 50,000 and 80,000. Yet it was only a little over 3,000. I entered the numbers again a few times but got the same answer. (Yes, I know the quote that says doing the same thing over and over again and expecting a different result is insanity, but I wasn’t entering the numbers incorrectly.)
I did discover what the problem was. The output on the screen was missing the leading digit, the first number in the result. I slid the result to the right and got this:
I have no idea why the app shows so many significant digits (also called significant figures). You might want that many to check the algorithm against a gold standard to see if it works well. For any real life purpose, you don’t need that many – well, maybe you do if you’re a NASA scientist.
I think that it makes it harder to really understand a number if it’s too complex. When you read about something like government spending, the numbers are rounded off. For example: “The program will cost $12.2 billion.” The report does not state the amount to the nearest dollar or cent.
My concern is much deeper. I am numerate and checked the result. But what if, for example, I had been determining how much fuel a plane needed and converting gallons to litres. An error like the one I’ve secribed could be catastrophic – all because the programmers were showing off how many digits they could include in the calculation. I can imagine that some less numerate people would think that since the app showed all those numbers, it must be very accurate and trustworthy – and they would simply accept what the screen shows without question.
I guess I could have found something online that would have directly converted km to miles – but how would I know if that was correct? And I realise that the speed in km/h was only shown to a whole number. So although 161 km is over 100 miles, it’s barely more: 100.04. So depending on how the speed is rounded, we may not have quite reached 100 mph. Back to the app. I need to be more careful when I choose what to download. This app is dangerously misleading. I think it does the arithmetic correctly (I did the long division and the first seven digits are right) but the presentation is seriously flawed. Beware!