Bench notes

Four explanations that would otherwise have to appear on three tool pages each. Prose, not calculators, and every figure in them checkable by hand.

Educational arithmetic only. Not medical advice and not a dosing protocol.

Displacement and the ceiling
Why a derived strength is an upper bound, and how much that is worth worrying about.
Rounding to the nearest mark
Half a graduation as a percentage of the draw, at nine volumes.
The thousand-fold error
Milligrams against micrograms, and the three things on this bench that stop the mix-up.
What a label does not say
The four things a correct answer still does not know.

What the bench will not tell you

This is educational arithmetic on figures entered by the reader. It is not medical advice, not a dosing protocol, and not a recommendation that anything be prepared, obtained or administered.

Nothing here states what quantity is appropriate for anyone, and there is no function in it that produces an amount to administer. A question about anyone’s health belongs with a licensed clinician who can examine the person asking.

Compounds of the kind this arithmetic is used on are largely research chemicals that are not approved by the FDA for human use. An exact calculation is not an accurate measurement: what is actually in a syringe depends on the preparation and the device, neither of which this page can see.

No qualified clinical reviewer is recorded against this site, and no credential is claimed anywhere on it. the limits of this bench.

What makes something a note rather than a tool

A tool takes figures and returns a figure. A note explains why a tool behaves the way it does, and it earns a page only when the same explanation would otherwise be repeated on three tool pages. There are four of them, and there is no fifth waiting to be written: the bench is small on purpose.

None of these pages asserts anything about a compound, a preparation or a body. They explain arithmetic and describe the printed properties of manufactured objects, both of which a reader can check with a calculator and a syringe.

The common thread

All four are about the gap between a calculation being exact and a measurement being accurate. Displacement is that gap at the mixing step. Graduations are it at the reading step. The thousand-fold error is it at the unit step. And the label note is the whole of what remains when all three have been handled properly, which is still more than the arithmetic ever contributed.