Answer:
To explain why \( (0.2) \times (0.002) = 0.0004 \), we can break down each decimal into its fractional form and then multiply the fractions.
First, let's express \( 0.2 \) as a fraction. The decimal \( 0.2 \) is equivalent to \( \frac{2}{10} \), because the digit "2" is in the tenths place.
Similarly, \( 0.002 \) can be expressed as \( \frac{2}{1000} \), because the digit "2" is in the thousandths place.
Now, we multiply the fractions:
\[ \frac{2}{10} \times \frac{2}{1000} = \frac{2 \times 2}{10 \times 1000} = \frac{4}{10000} \]
So, \( (0.2) \times (0.002) = \frac{4}{10000} \).
Now, we can simplify the fraction \( \frac{4}{10000} \):
\[ \frac{4}{10000} = \frac{4}{10^4} = 0.0004 \]
Therefore, \( (0.2) \times (0.002) = 0.0004 \).
