I guess to one billionth, because nothing can be measured to billionth decimal place.
surely that depends on the unit of measurement :-)
Only about 10^247 of instructions could have been performed by a computer since beginning of our universe (if the entire universe was converted into a computer and it would do calculations in theoretically optimal way).
The observable universe volume to planck volume ratio is only of the order of 10^185.
247, 185, that's still long way to 1000000000 orders of magnitude, whatever way to look at it.
Even if you decide your unit of measurement of volume is the volume of entire observable universe then the planck volume, which is orders of magnitude less than any particle volume, is still just 10^-185. That is just 185 decimal places, far from billion decimal places.
Or, in other words, if you like something more tangible: 0.00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 0000000000000000000000000000000001
This is 1 at 185th decimal place.
If I did this for 1 billion decimal places the entire document would be gigabyte in size and you would spend a bit of time downloading and scrolling it, assuming HN would first allow me to upload it.
Sure, but if your unit of measurement is (for whatever reason) 10^billion times the observable universe that statement holds.
I don't think any amount of pedantry will let us distinguish a billionth significant figure though.
According to Stirling's approximation, (10^185)! is more than 10^10^187, which makes a billion decimal places look very small indeed.
The topic is an article saying "Precision studies of antihydrogen atoms, for example, have shown that their characteristics are identical to hydrogen atoms to beyond the billionth decimal place." This suggest the "characteristic" is some kind of physical property that can be measured and compared.
My immediate research only renders that it used to be this in British English
No offense meant but it's usually shown as an example of the "Americans can't count" stereotype: 1,000,000,000 is a thousand millions.
The American naming system uses roots more clearly and doesn't have the weird pointless bundling together of two groups of 3, but it has a bizarre off-by-one issue... and not the usual 0->1 or 1->0 issue, but a 1->2 issue. For consistency, the order ought to be "ones, millions, billions, trillions, quadrillions", so that the prefix on the digit counter indicates the number of factors of 1000 in question, from zero, one, bi=two, tri=three, etc. However, "thousands" get stuck in there wrecking the whole thing up, so where the names say you have 1 group of 1000, you in fact have two, and so on.
It's not an imperial vs. metric sort of thing, it's more an arguing which is the "real" temperature, Fahrenheit or Celsius, when in fact the answer is basically neither because the "real" temperature scale ought to have its 0 at absolute zero, like Kelvin [1] or the lesser-known Rankine [2], which is basically "Kelvin, except the degree is 1 degree Fahrenheit". These are both more "real" because now you can add and subtract temperatures meaningfully, which you can't do with either of Fahrenheit or Celsius. And likewise, neither number system is abstractly all that great. But then, that's part of why we have scientific notation.
[1]: Which I just learned is about to be redefined, as of May 20th, 2019: https://en.wikipedia.org/wiki/Kelvin#2019_redefinition
Unfortunately it is likely too late to really adopt the metric system for financial transactions. But the K has crept in for thousands.
milion = 10^6, miliard = 10^9
bilion = 10^12, biliard = 10^15
trylion = 10^18, tryliard = 10^21
kwadrylion = 10^24, kwadryliard = 10^27, ...
But I agree that writing 1.23 * 10^6 is preferable.
It's consistent, but it's consistent with something that doesn't match people's usage.
Both systems are roughly equally broken, so either side mocking the other for their number system is a display of parochialism above and beyond the usual levels one would see.
I respectfully offer the Lakh [1] (1,00,000) and the Crore [2] (1,00,00,000) for other things people care about. :)
[1] https://en.wikipedia.org/wiki/Lakh [2] https://en.wikipedia.org/wiki/Crore
4 is a more common grouping than either 3 or 6. All of China and Japan and many places in between group their digits in fours.
And I always group the digits of hexadecimal numbers in fours.
Hi. I live in Poland. We use "milion" and "miliard" which sound exactly as you would say them in english and somehow I never met anyone who would have problems distinguishing one from the other, phonetically. Soo... maybe not that stupid after all?
https://en.m.wikipedia.org/wiki/Long_and_short_scales#Curren...
“The traditional long scale is used by most Continental European countries and by most other countries whose languages derive from Continental Europe (with the notable exceptions of Albania, Greece, Romania, and Brazil).”
Million (10⁶)
Milliarde (10⁹)
Billion (10¹²)
Billiarde (10¹⁵)
etc.
10^6 : Million 10^9 : Milliarde (instead of billion) 10^12 : Trillion 10^15 : Quadrillion