4 ms·

How can a calculator have an innate number of sigfigs? Significant figures depend on on the number of digits of an input number

jacquesm 3y ago
No, it depends on the significant digits of the input number. And more often than not there are very few of those, even though it may look like there are a lot. And your average calculator has no idea about how to deal with this properly. A typical measurement (say, temperature) has two significant digits at best, three if you're very precise and have a calibrated thermometer operating in the sweet spot of its scale. A measurement of time is hard to achieve to better than 10/th of a second without special preparation and as the interval you are measuring gets longer so will the error (because they tend to accumulate). A measurement of weight is so tricky that even three or four successive measurements are going to give you different results. Modern personal weight scales fake this by freezing the digital output at some arbitrary value and if you get off the scale and back on again it doesn't do another measurement but it simply displays the stored value to give you the illusion of precision where there really isn't any, another measurement might be off by a few hundred grams. So for most problems that do not involve money but real world data the number of significant digits is very low. Two, three, maybe. Four in very rare cases. And when you start combining them you're quickly into 'order of magnitude' territory rather than anything precise.
- alan-hn 3y ago
  Right, that's what I was saying. Which is why I was wondering about the claim that I'm replying to saying that a calculator itself has a specific number of significant digits independent of the input numbers
  - jacquesm 3y ago
    I think what they're getting at is that it has 11 digits internally but only displays the significant ones even though it has more 'under the hood'.

jacquesm 3y ago

No, it depends on the significant digits of the input number. And more often than not there are very few of those, even though it may look like there are a lot. And your average calculator has no idea about how to deal with this properly. A typical measurement (say, temperature) has two significant digits at best, three if you're very precise and have a calibrated thermometer operating in the sweet spot of its scale. A measurement of time is hard to achieve to better than 10/th of a second without special preparation and as the interval you are measuring gets longer so will the error (because they tend to accumulate). A measurement of weight is so tricky that even three or four successive measurements are going to give you different results. Modern personal weight scales fake this by freezing the digital output at some arbitrary value and if you get off the scale and back on again it doesn't do another measurement but it simply displays the stored value to give you the illusion of precision where there really isn't any, another measurement might be off by a few hundred grams. So for most problems that do not involve money but real world data the number of significant digits is very low. Two, three, maybe. Four in very rare cases. And when you start combining them you're quickly into 'order of magnitude' territory rather than anything precise.

alan-hn 3y ago
Right, that's what I was saying. Which is why I was wondering about the claim that I'm replying to saying that a calculator itself has a specific number of significant digits independent of the input numbers
- jacquesm 3y ago
  I think what they're getting at is that it has 11 digits internally but only displays the significant ones even though it has more 'under the hood'.