To find the missing number in the equation \( 59 \times ? = 0.59 \), we can denote the missing number as \( x \).
So we need to solve the equation:
\[ 59 \times x = 0.59 \]
To find \( x \), we can divide both sides of the equation by 59:
\[ x = \frac{0.59}{59} \]
Now, let's do the division:
\[ x = 0.01 \]
Thus, the missing number is:
\[ \boxed{0.01} \]