What whole number must go in the box so that the list of values is in ascending order?

The first value is 0.3. To convert a decimal to a percentage, multiply by 100.

$$0.3 \times 100\% = 30\%$$

The second value is $\boxed{\phantom{X}}\%$. This is already in percentage form.
The third value is $\frac{32}{100}$. To convert a fraction to a percentage, divide the numerator by the denominator and then multiply by 100.

$$\frac{32}{100} \times 100\% = 32\%$$

The list of values in percentage form is $30\%$, $\boxed{\phantom{X}}\%$, $32\%$.
For the list to be in ascending order, the value in the box must be greater than $30\%$ and less than $32\%$.

$$30\% < \boxed{\phantom{X}}\% < 32\%$$

We are looking for a whole number that is strictly between 30 and 32. The only whole number that satisfies this condition is 31.

The whole number that must go in the box is $\boxed{\text{31}}$.