Lies, Damned Lies and Decimal Places

There was a certain amount of noise in some parts of the Twittersphere yesterday, regarding the growth figures.
The growth figures last quarter indicated a 0.5% decrease in the economy. While for this, the growth figure was an increase of 0.5%. That meant it was back where it came from, said the pundits. Not so, said the twitterati. For if you subtract 0.5% and then add on 0.5%, that's not the same.

It's easy enough to show that this is true if you use a very large decline and increase. Suppose the economy is 100, and it declines by 50% in one quarter. The economy is now (100*(100-50)/100) = 50. But then if the economy grew by 50% in the next quarter, then it's now 50*(100+50)/100) = 75. So it's not where it came from, is it? QED.

But that's with a large increase. Let's do the same with a small decrease and then increase. So for 0.5% decline, the economy will go from 100 to 99.5. And with the same increase, it will then go from 99.5 to 99.5*(100+0.5)/100. Which is 99.9975. Which is clearly not 100.0000. But it's a bit of a mouthful. So let's round it to 2 Decimal Places, shall we? Which makes it... Oh. 100.00. So it's not the same number, but yet it is. So you could say the economy has bounced back to not quite where it was, but it is, probably, within the margin of error, once you remember that Bernie did build that extension after all, and Waitrose sold 4 more jars of mustard than they expected.

So on a strict, strict, strict interpretation, with every number quoted to 4 decimal places, the pedants may well be right. But even if they are, who wants to be a pedant?