Solve Division Problem: 0.4 Divided by 200

To solve the problem of dividing $0.4$ by $200$, we can follow the steps outlined below:

• Step 1: Convert the decimal to a fraction.
  $0.4$ is equivalent to $\frac{4}{10}$.
• Step 2: Set up the division as a fraction.
  The division $0.4 \div 200$ can be rewritten as $\frac{4}{10} \div 200$. This is the same as multiplying by the reciprocal of $200$, thus $\frac{4}{10} \times \frac{1}{200}$.
• Step 3: Simplify the fraction.
  Multiply the fractions: $\frac{4 \times 1}{10 \times 200} = \frac{4}{2000}$.
• Step 4: Simplify further if possible.
  Divide the numerator and denominator by the greatest common factor. The greatest common factor of 4 and 2000 is 4.
  Thus, $\frac{4}{2000} = \frac{1}{500}$.
• Step 5: Convert the simplified fraction back to a decimal.
  The fraction $\frac{1}{500}$ in decimal form is $0.002$.

Therefore, the solution to the problem is $0.002$.