Which of these is the largest?

Explanation

1. 01

   $\frac{3}{7} \approx 0.4286$ and $\frac{4}{9} = 0.4444\ldots$

2. 02

   So $\frac{4}{9}$ is the largest, ahead of 0.43, $\frac{3}{7}$ and 0.42.