The discussion centers on the significance of trailing zeroes in decimal numbers, particularly in the context of measurement accuracy. It is established that in a measurement like 2.34000g, the trailing zeroes indicate the precision of the measuring instrument, which in this case can measure to five decimal places. Therefore, all digits, including the trailing zeroes, are considered significant figures, as they reflect the accuracy of the measurement. This distinction is crucial for scientific reporting, as it communicates the level of precision and potential variability in the measurement.
PREREQUISITESStudents, scientists, and professionals in fields requiring precise measurements, such as laboratory technicians, engineers, and researchers in physical sciences.
Leoragon said:What do you mean tell us the accuracy? Isn't 2.34 already accurate enough?
If I'm getting this right. The extra zeroes just tells me the capabilities of the instrument.
Leoragon said:I still don't get it.
Leoragon said:What do you mean tell us the accuracy? Isn't 2.34 already accurate enough?
If I'm getting this right. The extra zeroes just tells me the capabilities of the instrument.
Leoragon said:Why are zeroes following a non-zero number in the decimal area considered significant?
2.34000 <-- Like this, why are the three zeroes after the four considered significant?
Borek said:I think you are just confused by the fact these digits are zeros.
You feel like 2.34 and 2.3400 mean the same... OK, now is there a difference between 1.06 and 1.0614? Sure there is.
Trick is, it is exactly the same thing. 2.34 (2.3400) is a weight in pounds, 1.06 (1.0614) is a weight of the same object given in kg. It is just obvious 14 means something.
symbolipoint said:Why do you want to assume that those zeros are significant? Either they are or they are not. Where is the number? From what is it taken or found? 2.34000 is more accurate than 2.34. Does that help? If we add 0.00001 to 2.34000 then we obtain 2.34001.
If we have 2.34 and add to it 0.0001, then we still have 2.34. Does that also help?
The "significant figures" are meaningless here. "Significant figures" are not a "math" topic, they are a "science" topic. You only use them to say how accurate a measurement (or quantity calculated from measurements are. If I say that a measurement is "3.5 m" I am saying that I am measuring to the "nearest tent meter" and the actual value could be anywhere from 3.45 m to 3.55 m. If, instead, I say "3.5000" meters, I am saying that I am measuring to the nearest tenth millimeter and the actual value could be anywhere from 3.49995 m to 3.50005 m.Leoragon said:First guy, I just picked a random number. Not something in pounds or kilograms or anything. It's just random.
No. As I said before "significant digits" have nothing to do with "numbers" per se. They only have to do with accuracy of measurements. Although I refuse to use the word "infinite", it is certainly true that there are an arbitrary number of different accuracies I could use in lengths and it is certainly possible that the distance I am measuring is smaller than the specific accuracy to which I am measuring. In that case I would say that I to "0" to the accuracy I was using.Second guy, I read in a book that the zeroes are significant. But what I keep getting is that the extra zeroes after the decimal are significant to show that those digits are indeed zero, not some other number; it removes the possibility of a different number. If that is true, then there can be an infinite number of significant numbers that are zero?