Significant figures between SI and non-SI units

Question

A person is running 10 km, and wikipedia states a US land mile corresponds to 1609.344 m. Would it be more sensible to express the results as 6.21 miles or 6 miles?

The salient point I recognize here is the conversion is between data of SI and non-SI based units.

Answer 1

The number of digits used to express the number should reflect the precision. Assuming that the '$0$' in '$10 \text{ km}$' is a significant digit, the precision is roughly $\pm 0.5 \text{ km}$, or $\pm 0.3 \text{ mi}$. Expressing it as $6.2 \text{ mi}$ suggest a precision of about $\pm 0.05 \text{ mi}$, so normally the most appropriate way to write it would be $6 \text{ mi}$. If you have reason to believe that the precision is greater, you could add decimal digits. That there is a conversion is not relevant, only the deduced precision is.

Answer 2

Writing quantities as integer numbers ending by zero should be avoided, because it is not clear how many significant figures are implied. Anyway, supposing $10$ km has $2$ significant digits (which is quite reasonable), I'd convert that to $6.2$ miles.