Words of wisdom from my college slide rule instructor:

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Calculators can provide precise answers up to 15 decimal places, but they are prone to floating point errors beyond that limit. The accuracy of a calculator's output depends on the context in which it is used, as it lacks the contextual understanding that a human has. For example, when dividing 1 by 3, a calculator will return a long decimal, but it does not differentiate between numerical values and measurements, which can lead to misunderstandings in interpretation.
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"A calculator is a thing that will give you the wrong answer to 15 decimal places."
 
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Ha I like that.
 
Well technically, it will give you the right answer to 15 decimal places as long as you know what to make it do. After 15 decimal places, it will give you the wrong answer due to floating point errors.
 
Calculators don't have all the information that you do. If you divide 1 by 3. It doesn't know if you're giving it measurements or just numbers, so it's going to give you lots of decimal places.
 
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