In a situation in which data are known to three significant digits, we write 6.379 m = 6.38 m and 6.374 = 6.37 m. When a number ends in 5, we arbitrarily choose to write 6.375 m = 6.38 m. We could equally well write 6.375 = 6.37 m, “rounding down” instead of “rounding up,” because we would change the number 6.375 by equal increments in both cases. Now consider an order of-magnitude estimate, in which factors of change rather than increments are important. We write $500 m$ ~ $10^{3}$ m because 500 differs from 100 by a factor of 5 while it differs from 1 000 by only a factor of 2. We write 437 m ~ $10^{3}$ m and 305 m ~ $10^{2}$ m. What distance differs from 100 m and from 1000 m by equal factors so that we could equally well choose to represent its order of magnitude as , $10^{2}$ m or as , $10^{3}$ m?