I'm going to take a different tactic for a moment. You are looking at serious precision. However, sometimes it does more good to look ahead to the end of your journey to be sure that you aren't wasting your time. Or making more work for yourself at the point when your computations are done and the real world steps into the picture.
So... you have these numbers computed to extreme precision. What are you going to do with them? Let me explain the point I want to make. If these numbers go to a bank, what is the limit on what they will take? If you offer your data to a bank or other financial institution, they will probably have a stated policy on how many decimal points they will retain. Most banks in the USA will draw the line at mils - i.e. thousandths of a dollar. Some might go as far as tenth of a mil. If you retain more digits than they do, you will almost surely come up with different answers than they would. And remember that if there is a discrepancy in a computation, the bank is arrogant enough to say that they are right and you are wrong. Big business gets like that.
It is commonplace for a requirement to "draw the line" at how many digits a business will keep. See, for example, Access data type "Currency" - which is a scaled integer that draws the line at 0.1 millidollars. There is a quote from one of the Civilization offshoots - "Civilization: Beyond Earth" - where the game makes the snide remark about people computing things
to many degrees of vacuous precision.
The question Dave (CheekyBuddha) asked earlier is relevant.
Are you plotting inter-planetary flight paths? If you are not, you are probably making incorrect assumptions over what you really needed.
If this is a monetary computation, you have to ask at what point your "partners in crime" will accept numbers. You would do better to limit your work to their standards. Is it a manufacturing process with precise tolerances? Vernier calipers or servo-motors have limited physical precision. You could measure the size of a physically holdable object in units of angstroms (= 0.1 nanometers, 10 digits, and the estimated size of simple molecules) and still have more digits than you need. Are you cutting something to a precise amount? The limit of precision is the width of the cutting device's narrowest cut. Don't expect micrometer tolerances in the hull of a battleship. Are we talking industrial chemistry? The scales used to measure bulk components to be mixed rarely need to go farther than grams, though milligrams are easy and micrograms are possible. But micrograms is only six decimal places. The real world isn't usually that precise.
The most precise clock on Earth is the Cesium 137 (so-called) "fountain" clocks, which actually DO have 16 digits of precision. That level of precision, however, means they are accurate to 1 second per 100-300 MILLION years (apparently, depending on specific brands of such clocks). And they all work using integers, by the way. An atomic clock works by counting atomic oscillation - yes, INTEGER counting - for things that vibrate at the atomic level at rates of 10,000,000,000,000,000 times per second, or frequencies of 10 quadrillion Hz. Though there is talk of a newer design that might make it to 10 QUINtillion Hz. In the prefixes, 10 QUADrillion is 10 PetaHz and 10 QUINtillion is 10 ExaHz. (I'll be honest, I had to look up that prefix because I don't usually work at the Peta/Exa level.)
Thanks, I need to pick limits to work with & they're going through several multipliers, being converted to percentages & multiplied against each other. So compounding has a massive effect very quickly after the decimal place
But you are looking at the wrong end of the telescope. The farther to the left you get, the bigger the significance of the digits you keep. Once you get past a certain point to the right, the digits become insignificant in every sense of the word. Even if you are dealing with devalued currency, the worst currency in the world today is the Lebanese Pound, which trades at about 123,000 LBP (rounded) to the dollar. OK, so you need six extra digits when computing exchange rates for that. But 16 digits? Let's say that the base unit has fractional currency for four places. Their exchange rate is over 100,000 to 1 with dollars. That's another six places. What are you going to do with the remaining 6 fractional digits?
In summary, my advice is (a) to recognize that if you want X digits of precision, you have to START with X digits of precision including any numeric constants involved in scaling or interest computations, and (b) past a certain point, I GUARANTEE you that unless you are working with Cesium atomic clocks or devices of extraterrestrial origin, there will be physical or policy limits on how many digits of precision you CAN use. And my point (b) is actually the point you should examine first as it colors what you have to do with point (a) at the start of your end-goal project.
Consider this as a commentary on the philosophy of precision.