How good is your accuracy? For example, if you are measuring the fine structure constant whose current accepted value is ~7.2973525693(11) x 10^(-3), then an error in the fourth decimal place matters. You'd be claiming a reasonably large deviation from the accepted value.

On the other hand, if you are measuring the parallax to Alpha Centauri, whose current accepted value is 750.81 ± 0.38 mas, then an error in the fourth decimal place simply does not matter.

And if you are doing something like "express 1/13 in decimals" and write 0.07693 instead of 0.07692, it's not something to worry about - in fact if someone attempts to duplicate your results, there's a good chance they get something similar but not exactly the same, simply because of rounding errors. Perhaps they rounded an earlier result and you didn't, for example. It only starts to matter when the precision is good enough that the difference should not be there.

How good is your accuracy? For example, if you are measuring the fine structure constant whose current accepted value is ~7.2973525693(11) x 10^(-3), then an error in the fourth decimal place matters. You'd be claiming a reasonably large deviation from the accepted value.

On the other hand, if you are measuring the parallax to Alpha Centauri, whose current accepted value is 750.81 ± 0.38 mas, then an error in the fourth decimal place simply does not matter (and you should not report it in the first place).

And if you are doing something like "express 1/13 in decimals" and write 0.07693 instead of 0.07692, it's not something to worry about - in fact if someone attempts to duplicate your results, there's a good chance they get something similar but not exactly the same, simply because of rounding errors. Perhaps they rounded an earlier result and you didn't, for example. It only starts to matter when the precision is good enough that the difference should not be there.

How good is your accuracy? For example, if you are measuring Newton's Gravitational Constant whose current accepted value is ~6.67430(15) × 10^(−11) in SI units, then an error in the fourth decimal place matters. You'd be claiming a reasonably large deviation from the accepted value.

On the other hand, if you are measuring the parallax to Alpha Centauri, whose current accepted value is 750.81 ± 0.38 mas, then an error in the fourth decimal place simply does not matter.

And if you are doing something like "express 1/13 in decimals" and write 0.07693 instead of 0.07692, it's not something to worry about - in fact if someone attempts to duplicate your results, there's a good chance they get something similar but not exactly the same, simply because of rounding errors. Perhaps they rounded an earlier result and you didn't, for example. It only starts to matter when the precision is good enough that the difference should not be there.

How good is your accuracy? For example, if you are measuring the fine structure constant whose current accepted value is ~7.2973525693(11) x 10^(-3), then an error in the fourth decimal place matters. You'd be claiming a reasonably large deviation from the accepted value.

On the other hand, if you are measuring the parallax to Alpha Centauri, whose current accepted value is 750.81 ± 0.38 mas, then an error in the fourth decimal place simply does not matter.

And if you are doing something like "express 1/13 in decimals" and write 0.07693 instead of 0.07692, it's not something to worry about - in fact if someone attempts to duplicate your results, there's a good chance they get something similar but not exactly the same, simply because of rounding errors. Perhaps they rounded an earlier result and you didn't, for example. It only starts to matter when the precision is good enough that the difference should not be there.