4 ms·

> just one order of magnitude off, on a 12-digit number Doesn't matter how many digits are involved; a factor of 10 is pretty significant.

thereisnospork 3y ago
Depends on the scaling factors. 10x the sound energy is only twice as loud.
- hgomersall 3y ago
  Only sounds twice as loud to a human observer.
wolverine876 3y ago
I don't know. The difference between 10^101 and 10^102 seems insignificant.
- Sebb767 3y ago
  Depends on context. The difference between 10^34 and 10^35 is the difference between a baby and a full-grown adult in planck sizes. For a more relevant example, a terrabyte is an unit we regularly work with that is ~10^18 bytes and an order of magnitude difference is still quite impactful (this is fewer orders of magnitude than your example, to be fair, but more than the original correction).
- rewmie 3y ago
  > I don't know. The difference between 10^101 and 10^102 seems insignificant. Pour yourself two cups of coffee. In one, add 10g of sugar. In the other add 100g of sugar. Do you think both are the same?
  - wolverine876 3y ago
    Compare the ratios of the exponents in your example and in mine. I see another consideration, an implication of the other response - the domain of the exponents. For example, consider 10^101 and 10^102: * The ratio of exponents is 102:101; not much apparent difference. * But that doesn't specify a domain, so maybe we implicitly assume the domain is (0, 1, 2, ... >= 102). However, if the domain is (100, 101, 102) then the difference between 10^101 and 10^102 seems more likely to be as significant as the difference between 10^1 and 10^2.
    - rewmie 3y ago
      > * The ratio of exponents is 102:101; not much apparent difference. I'm not sure if you understand why this is nonsense. A factor of 10 is not small by any scale, and the relationship between 1 ton and 100kg does not suddenly become insignificant if you decide to express weight in nanograms.
      - wolverine876 3y ago
        Maybe instead of calling each other's ideas nonsense, we could try to learn something. Maybe next time!

thereisnospork 3y ago

Depends on the scaling factors. 10x the sound energy is only twice as loud.

hgomersall 3y ago
Only sounds twice as loud to a human observer.

wolverine876 3y ago

I don't know. The difference between 10^101 and 10^102 seems insignificant.

Sebb767 3y ago
Depends on context. The difference between 10^34 and 10^35 is the difference between a baby and a full-grown adult in planck sizes. For a more relevant example, a terrabyte is an unit we regularly work with that is ~10^18 bytes and an order of magnitude difference is still quite impactful (this is fewer orders of magnitude than your example, to be fair, but more than the original correction).
rewmie 3y ago
> I don't know. The difference between 10^101 and 10^102 seems insignificant. Pour yourself two cups of coffee. In one, add 10g of sugar. In the other add 100g of sugar. Do you think both are the same?
- wolverine876 3y ago
  Compare the ratios of the exponents in your example and in mine. I see another consideration, an implication of the other response - the domain of the exponents. For example, consider 10^101 and 10^102: * The ratio of exponents is 102:101; not much apparent difference. * But that doesn't specify a domain, so maybe we implicitly assume the domain is (0, 1, 2, ... >= 102). However, if the domain is (100, 101, 102) then the difference between 10^101 and 10^102 seems more likely to be as significant as the difference between 10^1 and 10^2.
  - rewmie 3y ago
    > * The ratio of exponents is 102:101; not much apparent difference. I'm not sure if you understand why this is nonsense. A factor of 10 is not small by any scale, and the relationship between 1 ton and 100kg does not suddenly become insignificant if you decide to express weight in nanograms.
    - wolverine876 3y ago
      Maybe instead of calling each other's ideas nonsense, we could try to learn something. Maybe next time!