What does "Ten-fold" mean?

In new reports you often hear the expression “a ten-fold increase” or five-fold etc.

Take this report as an example: BBC News - Stay-at-home fathers 'up 10-fold'

I was taught by my maths teacher that ten times and ten-fold have different meanings.

Ten fold 60,000 is actually 61,440,000 not 600,000 and this is why:

When you fold something you effectively double it, think of folding a piece of paper. If you fold a piece of paper once you have 2 layers, fold it again and you have four layers and so on.

So if you “fold” 60,000 you have 120,000, fold it again and you have 240,000 and so on. After “folding” it ten times you have a figure of 61,440,000.

Please discuss :-).

both of these say having 10 parts or 10x as many

I don’t know the origin of the phrase or your teachers interpretation but common usage goes with 10 times

It’s nothing much to do with folding of anything - the ~fold suffix comes from old English and just means ‘of (or divisible into) x many parts’ - so fourfold means ‘of four parts’. Manifold means ‘of many parts’

The potential for misunderstanding isn’t really anything to do with the term - it’s just that ~fold tends to be used exclusively with ‘increase’, so a threefold increase is the same as a 300% increase, or in total, four times the original amount.

Ten fold means ten times, so 600,000 is a tenfold increase over 60,000. What you’re describing is raising something to the tenth power.

This is the first time I’ve ever run across that theory! Whenever I’ve seen or heard a word like “tenfold” used, it means either “ten times” or “having ten parts”; and the definitions I’ve managed to Google up just now agree.

I was going to say that the “-fold” suffix doesn’t have anything to do with the verb “to fold,” but upon checking, it looks like they have the same origin (-fold; fold), so maybe there is an etymological connection there somewhere.

“Fold” in this sense has nothing to do with folding paper over. Folding is equivalent to exponentiation, not multiplication. Your sum is** 60,000 × 2[sup]10[/sup]**, which is not an accepted definition of “increasing 60,000 tenfold”.

Not quite - 60,000[sup]10[/sup] would be about 6 x 10[sup]47[/sup]. The OP multiplied by two to the tenth.

Nope, - fold (Old English - feald) as a suffix or numeric modifier just means “times” - as in fourfold (four times), or hundredfold (one hundred times).

Fold (Old English faldan or fealdan) “to bend cloth back over itself,” describes the layered effect, not a doubling. There are plenty of ways to fold things without doubling.

Si

I think your maths teacher was the victim of some really odd urban legend.

I would assume that the mere fact most people can not quickly and easily perform this calculation in their head would make it unlikely this interpretation is preferable to a simple “times”.

On re-reading, I see I misread the nature of the disagreement (I thought it was a contest between 10 times and ‘increase by ten times itself’ - the latter of which may mean 11 times).

However, the definition of the ~fold suffix stands. Sounds like your maths teacher had his own special, non-standard definition.

Thanks for the replies, I know the general consensus if that ten-fold means ten times and five-fold means five times etc.

There does seem to be a bit of confusion about the term, here for example: http://www.blurtit.com/q577324.html

I am slowly being convinced that my maths teacher was incorrect, but I will wait for a little longer, it’s like being told that Einsteins’ theory or relativity is wrong :dubious:.

Also, why don’t people just use the term “ten times”?

I think your teacher was overthinking it. I have never heard that interpretation.

Because using “tenfold” as an adjective conveys the idea very economically and fluidly. The word works perfectly well for this. Getting the same thought across with the phrase “ten times” offers no improvement, and would either be awkward and confusing or require a whole lot more words.

Another possible reason is that, in some contexts, “ten times” could be ambiguous: does it mean “ten times as much” or “ten separate occurences”?

Middle English Dictionary for tenfold.

Yes, that would be the “confusing” part. And to clarify it takes a lot more verbiage.

You’re going to trust random internet posters, rather than the dictionary and hundreds of years of usage?

It’s NOT like being told Einstein theory of relativity was wrong.

It’s like being told Einstein’s theory of relativity really dealt with how his relatives were spread over Germany (hence relativity). If your teacher told you that, they’d be wrong. Same case here. The explanation is wrong - not the term or theory.

As I mentioned in another thread, some math teachers (and I imagine teachers, in general) do often give just plain bad information to students. They’re not infallible.

So far the confusion seems to lie with that poster, your math teacher, and you. I think it’s safe to say that the other 99.9+% of the world, including every actual authority on the matter, is not confused.

I’ve encountered something like the OP’s usage occasionally, for instance, in cosmological inflation, one often speaks of ‘60 e-foldings’, meaning an increase by e[sup]60[/sup]. So what the OP wants could be framed as ‘ten two-foldings’, and if the two is understood, I could see abbreviating that as ‘tenfold’. But if I encountered ‘tenfold’ in the wild, I’d assume it to mean ‘by a factor of 10’.