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What is the arithmetic to convert 10 mg in 5 mL into units on a U-100 scale?

Asked 21 Feb 2025Modified 14 months agoViewed 16k times
34

Conditions: 10 mg · 5 mL.

Please show the division. I want to check my own against yours.

I would like the general form as well as the specific number, so I can apply it again.

How many significant figures are actually justified here?

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EM
askedeoin_mcgarry16k1821 Feb 2025
8Thank you — the worked example is what makes this usable. – mz_4113 7 months ago
Related: the same reasoning applies to the counter-ion question. – Dr_Ingrid_Baumgartner 8 months ago
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5 Answers

Accepted answer first, then by votes
29

Accepted answer

More usefully, the distinction that resolves most of these questions is understanding what concentration actually means and why it is not the same as label claim.

On filtration: a 0.22 µm syringe filter will remove particulates and organisms, and it will also adsorb a fraction of your peptide onto the membrane — with a low-binding PVDF or PES membrane the loss is typically a few per cent.

Reading a lyophilised cake

AppearanceInterpretationAction
Intact opaque puck, proud of baseCycle ran correctlyProceed
Slumped to one sideShipped before fully dry, or vibrationUsually usable; note it
Glassy translucent filmCollapse above glass transitionTest before use
Melt-back ring at stopperThermal excursion in transitTest before use
No visible cake at allVery low fill, or nothing thereWeigh it; query the supplier

The underlying point is that the concentration you actually work with is label claim times content fraction divided by actual diluent volume, which is usually not the same as the nominal concentration because content is usually not 100 per cent and you rarely measure the diluent volume to 0.1 mL precision.

Published data on syringe dead space quantifies low-dead-space designs as retaining under 2 µL against 35 µL or more for conventional detachable-needle syringes.

Do the arithmetic twice, ideally with someone else doing it independently.

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MH
answered · acceptedm_haraldsen38k3831 May 2025
8Thank you — the worked example is what makes this usable. – Dr_Elias_Weiss 3 months ago
Related: the same reasoning applies to the counter-ion question. – Dr_Bram_Verhoeven 5 months ago
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34

Write the units at every step, because units errors are the failure mode that catches everyone eventually.

Breaking it down further: if a 10 mg vial has 96.5 per cent content, you have 9.65 mg of peptide. Divide that by 2.00 mL and your concentration is 4.825 mg/mL, not 5.00 mg/mL, which is a 3.5 per cent systematic error in every dose calculation.

Worked example, because the general form is easier to trust once you have seen it once. Take a 10 mg vial and add 2 mL of diluent: the concentration is 10 ÷ 2 = 5 mg/mL. A 0.5 mg dose is 0.5 ÷ 5 = 0.1 mL. On a U-100 syringe, where 1 unit = 0.01 mL, that is 0.1 ÷ 0.01 = 10 units. Change the diluent to 1 mL and the same dose becomes 5 units — same dose, half the resolution.

The insulin-unit standard U-100 means 100 units per millilitre, so one unit is 0.01 mL — this is the conversion that trips up more people here than any other single piece of arithmetic.

Worth noting: the concentration after reconstitution is not the same as the label claim, and most people do not account for the difference.

Write the arithmetic on the vial label. It costs nothing and removes the step where you reconstruct it from memory.

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DF
answeredDr_Colm_Fitzhenry85k24823 Feb 2025
22

Work in the order concentration, then volume, then units, and the arithmetic stops being confusing. Concentration is milligrams per millilitre and comes from the vial contents and the diluent volume. Volume per dose is dose divided by concentration. Units on a U-100 syringe are volume in millilitres multiplied by one hundred.

Dead space quantified: a fixed-needle insulin syringe holds roughly 3 to 5 µL in the hub and needle after the plunger bottoms out. A luer-lock syringe with a detachable needle holds 35 to 100 µL depending on the hub design. At 5 mg/mL that is 15 to 25 µg lost per draw on the insulin syringe and 175 to 500 µg on the luer-lock — which over ten draws is the difference between losing a rounding error and losing half a milligram.

Mechanically, do not use the same needle to pierce the stopper and to administer. The tip is blunted by the stopper, and the hub now contains a dose you are about to lose to dead space anyway.

The content assay results from major testing services show that nominal vial claim and measured content differ by one to ten per cent, making content a driver of dose error.

The limitation is that technique reduces risk, it does not remove it, and nothing you can do outside a controlled environment makes a non-sterile preparation sterile.

If in doubt, use more diluent and accept the shorter usable window.

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FC
answeredfiadh_cronin14k286 Mar 2025
Do you have a reference for the last claim? Not disputing it, just want to read it. – thabo_maseko 8 months ago
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12

The common error is getting the concentration right but then misreading the syringe scale, which is why checking the barrel marking rather than your memory matters.

Number of stopper piercings matters less than the gauge doing the piercing. A 30G or 31G needle through a butyl stopper leaves a track that reseals; a 21G or 18G drawing needle punches a core and can drop it into the solution.

The Arrhenius relationship for drawing kinetics means that cold solution takes noticeably longer to draw than room-temperature solution.

Do the arithmetic twice, ideally with someone else doing it independently.

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SL
answeredsian_llewellyn85k24812 Jun 2025
10

Rounding to the nearest whole syringe unit is usually the right error to make, but understanding which direction it is and why matters.

The rounding error accumulates if you round too many times — rounding concentration to 5.0, rounding the dose volume to 0.1 mL, rounding the unit reading to 10 — and the safest approach is to work the full precision and round only the final answer.

One qualification: if your arithmetic and someone else's disagree by a factor of ten, one of you has made a unit error, and writing out the units at every step is the diagnostic.

Write the arithmetic on the vial label. It costs nothing and removes the step where you reconstruct it from memory.

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DO
answeredDr_Lena_Ostrowska42k388 Apr 2025

Your answer

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