By extracting positional values to map variables correctly, the evaluated sum of the expression 5A + 3B + 6C + D + 3E corresponds to the computed total of 53.6003.

The decimal values are: 2/3 ≈ 0.667 (smallest) and 5/6 ≈ 0.833 (biggest). Subtracting the smallest from the biggest: 5/6 - 2/3 = (5 - 4)/6 = 1/6.

The exponent 1/2 is equivalent to the principal square root. The square root of 100 is 10, because 10 * 10 = 100.

Multiply numerator and denominator by sqrt(7) to rationalize. The numerator becomes 2*sqrt(7) and the denominator becomes 7, creating the fraction 2*sqrt(7) / 7.

The product rule applies to any number of terms with the same base. Adding the exponents 3, 4, and the implicit 1 gives 3 + 4 + 1 = 8, yielding a^8.

To successfully mold the number into correct scientific format, the decimal point gets shifted precisely 8 spots toward the left side, making it equal 5.18 * 10^8.

Using the law of exponents for multiplication, we keep the base the same and add the powers. For 3^4 * 3^2, adding the powers 4 and 2 gives us 3^6.

Each fraction takes the form of (n-1)/n, meaning its difference from 1 is 1/n. Since 1/16 is the largest difference among the choices, 15/16 falls farthest below 1, making it the smallest fraction.

Evaluating them gives: 3/8 = 0.375, 5/13 ≈ 0.385, 2/5 = 0.400, 4/9 ≈ 0.444, 6/11 ≈ 0.545. The sorted list is 3/8, 5/13, 2/5, 4/9, 6/11. The fourth element in this sequence is 4/9.

The given bounds evaluate to 0.600 (3/5) and 0.667 (2/3). Converting the options: 2/5 = 0.40, 1/3 ≈ 0.33, 1/15 ≈ 0.067, and 31/50 = 0.62. Only 31/50 correctly fits into the range.