To find the ratio of sneakers to flat shoes, we first need to determine how many pairs of each type Marsha has.
- Number of pairs of sneakers: 3
- Number of pairs of flat shoes: 8
Now, we can express the ratio of sneakers to flat shoes as:
\[ \text{Ratio} = \frac{\text{Number of pairs of sneakers}}{\text{Number of pairs of flat shoes}} = \frac{3}{8} \]
Next, we calculate this as a decimal by dividing 3 by 8:
\[ \frac{3}{8} = 0.375 \]
Finally, we round 0.375 to the nearest hundredth. Since the third decimal place is 5, we round up:
\[ 0.375 \text{ rounded to the nearest hundredth is } 0.38 \]
Thus, the ratio of sneakers to flat shoes, represented as a decimal and rounded to the nearest hundredth, is \( \boxed{0.38} \).