What does it mean that
The same number of decimals after the "." does not mean the same number of significant figures. (41.5821 = 6 significant figures; 0.0010 = 1 significant figure)?
This is a good question, often misunderstood, abused, avoided, and seldom adhered to. Computer and digital computers and calculators often spit out a laundry listing of figures, and it is hard to tell sometimes what is being said when these are reported. In your first example, the numbers suggest 6 significant figures. The second example to me suggest 2 significant figures, the 1 and the 0 following the one. If the report said 0.001, then that would be one significant figure. Don’t add zeros after the first number beyond the decimal unless significant. Before the decimal sometimes 0 hold places of units, tens, etc. So 1000 has 1 significant figure. But if reported as 1000.1, there are 5 significant figures. Sometimes scientists report large numbers using powers of ten, such as 6.02 x 10^23, and sometimes small numbers seem to have too many significant figures such as Pi is 3.14...... Sometimes we just report too many numbers, disregarding significance, such as if I take my time and measure a stream carefully and add up all the figures to be 104.65 cubic feet per second. At best I know the value on a good day is plus or minus 10%, so I should probably report 100 cfs. But when I plot the value on the stage discharge curve, I would probably use 105 cfs, especially if using log paper. When we were spraying pesticides, I has them add rhodamine B dye to the mix at a calculated rate, and used a fluometer to measure concentration of dye, and from that estimate concentration of pesticide. Although data can sometimes read out with several figures, one must decide how many are apt to be significant. In this instance, if amount detected showed a likelihood of pesticide contamination, I would send the bottles to the lab for more costly testing. I’m probably at fault as much as anyone else, but cognizant that 2-3 significant figures are usually overkill, but if dealing with distances, latitude-longitude and some other subjects, sometimes you can have a boatload of significant figures to deal with.
@ William F. Hansen Thank you, Sir
while reporting any result, like 2.345 ± 0.01 is fine or we should report 2.345 ± 0.01000?
I mean to say the same numbers of significant figures are required in the mean value and in the standard deviation value (while reporting mean± SD)?
No, 41.5821 is actually 4 significant figures because you only count after the dot with rational number. The principle and purpose of significant figures really relates to fractions of whole numbers, not really the whole numbers themselves (unless it's a rational number that is rounded to a whole number). So, 0.0010 is 4 significant figures too – the last 0 shows that the fifth number after the dot is 0–4 with rounding. So the number of decimals after the dot always means the same thing in all cases imo :)
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