The number of ions that enter each meter of the axon is 5.5 x 10^11. Each of these ions has a charge, given by +e, which is equal to 1.6 x 10^-19 Coulombs. The time during which these ions enter the axon is 13 milliseconds, or 13 x 10^-3 seconds.
To solve this problem, first, we need to calculate the total charge that has been transferred. This is found by multiplying the number of ions by the charge of each ion. Hence, the total charge, q, is (5.5 x 10^11) * (1.6 x 10^-19) = 8.8 x 10^-8 Coulombs.
Knowing that the definition of current, I, is the charge transferred per unit time (I = q/t), we can find the current by dividing the total charge by the time. This gives us I = (8.8 x 10^-8) / (13 x 10^-3) = 6.769 x 10^-6 Amperes.
However, the question requests the answer to be expressed in micro Amperes. As we know, 1 A = 10^6 uA. Hence, our final answer is (6.769 x 10^-6) * (10^6) = 6.77 uA.
Therefore, the current during the inflow of charge in a meter of the axon, with two significant figures, is 6.77 uA.