Letting the positive number be x and then expressing the first condition in terms of x, we get:
2/3 x = 16/216 * 1/x
We can then multiply both sides by 216 and simplify to get:
x^2 = 16/144
Taking the square root of both sides gives:
x = sqrt(16/144)
Simplifying this expression gives:
x = sqrt(1/9)
Finally, since the number must be positive, we take the positive square root, which gives us:
x = 1/3 or 4/12
Therefore, the positive number that satisfies the given conditions is 1/3.