Does 1 + 1 always equal 3?
No.
If you do not give all of the medication in a syringe, vial, ampule, you are rounding off. This is where significant figures matter.[1]
1+1 does equal 3 for sufficiently high values of 1.
For those who do not understand this –
Consider a morphine syringe with a volume of 1 ml that contains a total dose of 10 mg.
We intend to give 1 mg.
Can we give exactly 1 mg?
I cannot.
We give an approximation of 1 mg.
What is considered to be 1 mg?
0.50001 mg should be rounded to 1 mg if we are not using decimal places. We probably do not have the precision to measure that accurately. If we did, we should use all of the significant digits in our documentation.
I am using this as an example to point out that with no decimal places 0.50001 mg is 1 mg.
We round off to the nearest significant digit.
If we are not using decimals, then 1.49999 mg is also 1 mg.
We will not be measuring that as carefully, either.
What we will be doing is trying to get close to 1 mg, but that could be 1.4 mg, or 1.3 mg, or 1.2 mg, or 1.1 mg, 0.9 mg, or 0.8 mg, or 0.7 mg, or 0.6 mg, or 0.5 mg.
How precisely can we measure the amount?
If we tend to underestimate the doses we are giving, we could be giving a couple of doses of 1.3 mg.
1.3 + 1.3 = 2.6, which is rounded to 3.
1 + 1 = 3.
If I gave 1.3 mg and 1.3 mg to the same patient, I gave 1 mg + 1 mg and the
1.4 can be rounded off to 1.
If there are no significant digits beyond the 1, then the value of 1 is anywhere from 0.6 to 1.4.
Add a couple of 1s that add up to 2.5, or greater, and you have 3.
1.2 + 1.3 = 2.5, which is rounded to 3.
When rounded to one significant digit, 1.2 = 1, 1.3 = 1, 1.4 = 1, and 2.5 = 3.
That is not what we generally think of when we think of 1 + 1 = 3.
We assume a precision that may not be there.
Error bars do not always result in excess.
We can end up with a small number due to wide error bars.
1+1 can equal 1 for sufficiently low values of 1.
So,
how
accurate
are
we?
–
Footnotes:
–
[1] Significant figures
Wikipedia
Article
.
This is not a real issue given two things: first that we use the proper equipment (i.e. syringe) to administer the dose, and second that we understand the reason behind significant digits.
With the typical 1cc syringes that I’ve used, nobody should be reporting morphine dosages (assuming 10 mg/ml) to only one significant digit; the device has more precision than that (usually marked to 0.1 or 0.2 ml divisions) If someone is reporting only one significant digit, it’s a reporting error, not a dosage error.
… which is probably your whole point…um…never mind.
mpatk,
I was thinking in terms of mg, not ml.
My morphine syringes are marked in 0.1 ml (1 mg) amounts.
I can honestly give 1 mg morphine and 1 mg morphine and have the patient receive 3 mg morphine. Our errors should be in the patient’s favor.
I am more interested in the accuracy of the degree of precision that we claim in documentation.
Then there is the use of significant, which can be mathematically (statistically) significant, while still not being clinically significant.
.