I am writing a program(this is not a programming question) this program calculates how small an inch needs to get until it reaches 1 Planck Length of an inch. I know there are 1,587,999,999,999,999,744,856,664,160,920,216 Planck Lengths in 1 inch, now i need to have a thing in my code that tests when a number gets smaller than 1 of how many Planck Lengths in 1 inch. Its hard to explain and this question may be removed to do not explaining correctly but i have no idea how to get this. Also this wont let me tag my question properly since i don't have 1000 rep so if this gets taken off for incorrectly tagging, don't blame me, it won't let me tag it for "planck" or "length" and not even for "inch".
2025-01-13 02:15:29.1736734529
How much of 1 Planck Length goes into 1 inch?
1.2k Views Asked by Cubit-Games https://math.techqa.club/user/cubit-games/detail At
1
I think you're experiencing rounding error with your number.
The measured value of the Planck length is only to about six significant figures:
$$L_P \approx 1.616199(97) \cdot 10^{-33} cm.$$
The numbers in parentheses indicate measurement error in the last significant figure (the last $9$) so it's $(1.616199 \pm 0.0000097) \cdot 10^{-33}$ cm.
Let's call the number out front $1.6162$.
Multiplying by $0.3937$ international inches per centimeter gives $L_P \approx 0.63629794 \cdot 10^{-33}$ inches, so there are $1.571591 \cdot 10^{34}$ Planck lengths per inch.
Now ... to get to your question. If you have something that's an inch long, and are shrinking it for some reason, you'll need to be able to keep track of a lot of significant figures. So you need some kind of arbitrary-precision arithmetic.
On the other hand, if you're making some kind of incremental thing that gives you logarithmic upgrades or something like that, you could just switch scales every factor of a million or so, and then just use regular double-precision.