The speed of light in vacuum is taken as unity. If light takes 6 min 40 s to reach the Earth from the Sun, the distance between the Sun and the Earth in new unit is: ____.

We are told that the speed of light is taken as the unit value 1 (distance unit per time unit). Therefore, in these new units the distance traveled by light equals the time it takes.

First convert the given travel time from minutes and seconds to seconds only.

$t\; =\; 6\backslash \; \backslash text\{min\}\; +\; 40\backslash \; \backslash text\{s\}\; =\; 6\; \backslash times\; 60\backslash \; \backslash text\{s\}\; +\; 40\backslash \; \backslash text\{s\}\; =\; 360\backslash \; \backslash text\{s\}\; +\; 40\backslash \; \backslash text\{s\}\; =\; 400\backslash \; \backslash text\{s\}$

Since the speed \(c\) is 1 distance unit per second, the distance \(d\) is

$d\; =\; c\; \backslash times\; t\; =\; 1\; \backslash times\; 400\; =\; 400$

Thus the distance between the Sun and the Earth, expressed in the new unit system, is **400**.