We need to find which of the fractions $\frac{399}{1000}$, $\frac{199}{500}$, $\frac{41}{100}$, $\frac{21}{50}$, and $\frac{3}{10}$ is closest to $\frac{2}{5}$.

1. Problem Description

We need to find which of the fractions $\frac{399}{1000}$, $\frac{199}{500}$, $\frac{41}{100}$, $\frac{21}{50}$, and $\frac{3}{10}$ is closest to $\frac{2}{5}$.

2. Solution Steps

First, we convert $\frac{2}{5}$ to a decimal: $\frac{2}{5} = 0.4$.

Now, we convert each of the given fractions to decimals:

(A) $\frac{399}{1000} = 0.399$

(B) $\frac{199}{500} = \frac{398}{1000} = 0.398$

(C) $\frac{41}{100} = 0.41$

(D) $\frac{21}{50} = \frac{42}{100} = 0.42$

(E) $\frac{3}{10} = 0.3$

Now we calculate the absolute difference between each fraction and $0.4$:

(A) $|0.399 - 0.4| = |-0.001| = 0.001$

(B) $|0.398 - 0.4| = |-0.002| = 0.002$

(C) $|0.41 - 0.4| = |0.01| = 0.01$

(D) $|0.42 - 0.4| = |0.02| = 0.02$

(E) $|0.3 - 0.4| = |-0.1| = 0.1$

The smallest difference is $0.001$, which corresponds to fraction (A).

3. Final Answer

(A) $\frac{399}{1000}$