Читать книгу Maths on the Back of an Envelope: Clever ways to (roughly) calculate anything - Rob Eastaway - Страница 19

I hope this opening section has demonstrated why, in many situations, quoting a number to more than one or two significant figures is misleading, and can even lull us into a false sense of certainty. Why? Because a number quoted to that precision implies that it is accurate; in other words, that the ‘true’ answer will be very close to that. Calculators and spreadsheets have taken much of the pain out of calculation, but they have also created the illusion that any numerical problem has an answer that can be quoted to several decimal places.

There are, of course, situations where it is important to know a number to more than three significant figures. Here are a few of them:

 In financial accounts and reports. If a company has made a profit of £2,407,884, there will be some people for whom that £884 at the end is important.

 When trying to detect small changes. Astronomers looking to see if a remote object in the sky has shifted in orbit might find useful information in the tenth significant figure, or even more.

 Similarly in the high end of physics there are quantities linked to the atom that are known to at least 10 significant figures.

 For precision measurements such as those involved in GPS, which is identifying the location of your car or your destination, and where the fifth significant figure might mean the difference between pulling up outside your friend’s house and driving into a pond.

But take a look at the numbers quoted in the news – they might be in a government announcement, a sports report or a business forecast – and you’ll find remarkably few numbers where there is any value in knowing them to four or more significant figures.

And if we’re mainly dealing with numbers with so few significant figures, the calculations we need to make to find those numbers are going to be simpler. So simple, indeed, that we ought to be able to do most of them on the back of an envelope or even, with practice, in our heads.