If 2/a, a/8, and 63% = 63/100 are in numerical order, then
2/a < a/8 < 63/100
Multiply each "side" of the inequality by 8a :
16 < a² < 126a/25
a has to be a whole number, and since 4² = 16, we must have at least a ≥ 5.
Divide through by a :
16/a < a < 126/25 = 5 + 1/25
Then at most, a ≤ 5.
So, both a ≥ 5 and a ≤ 5, which means a = 5.
Just to check that the list is in order, we have
2/a = 2/5 = 0.4
a/8 = 5/8 = 0.625
and 0.4 < 0.625 < 0.63.
