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For example, if we need an answer that is precise to 4 significant figures. Or, let's say it is the standard procedure to use 4 significant figures in a department in a company.

Say, if the probability of failure is 0.02441%, if we write it as the probability of success, then it is 99.98%. Now both are 4 significant figures, but the 0.02441% definitely is more informative than the 99.98%. For example, we can say 99.98%. Now is it 99.975% or is it 99.98499%? Both become 99.98% but the former gives a failure rate of 0.025% and the latter gives 0.01501%, and they differ a lot by percentage (0.01501 x 166% = 0.025), and it is far less information than what the number 0.02441% can provide.

In fact, if department A states it as 99.98% success, then department B can later quote that its failure rate is 0.02% (vs 0.02441%), reducing the failure rate by 20%, "scientifically and mathematically" correct.

So shouldn't there be an exception in this case, but is there a rule that says there should be an exception, and how many significant numbers should be provided -- and is there also a rule?

nonopolarity
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1 Answers1

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As you have discovered, if you want to know $1-x$ to four significant figures, you may need to know $x$ to a lot more than four significant figures if $x$ is close to 1.

So if a company has a rule that means they only store 4 significant digits of any number, they also have to outlaw subtracting numbers that are close to each other, or accept that such numbers will be far less accurate than 4 significant digits.

Kusma
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