What value should go in the empty box to complete the calculation for finding the product of 62.834 × 0.45? 62.834 times 0.45 gives two partial products. the first is 314170, and the second is unknown.

In this item, we are to supply for the missing term on one side of the equation. The left side is given to be composed of 62.834 x 0.45. The right hand side is given to be composed of 314170 along with a missing entity. 

Translating the given to mathematical expression and letting A be the unknown,
  62.834 x 0.45  = 314170 A

To determine the value of A, divide both sides of the equation by 314170.
             (314170A)/(314170) = (62.834 x 0.45) / 314170
                 A = 0.00009

The missing value is 0.00009 or 9.0 x 10^-5. 

I’d say letter a..