tyou know about decimals or fractions to explain why $$ (0.2) \cdot(0.002)=0.0004 $$

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To understand why $$ (0.2) \cdot (0.002) = 0.0004 $$, we can break it down step by step using decimals and fractions.

1. **Convert the decimals to fractions**:
   - $$ 0.2 $$ can be expressed as $$ \frac{2}{10} $$ or simplified to $$ \frac{1}{5} $$.
   - $$ 0.002 $$ can be expressed as $$ \frac{2}{1000} $$ or simplified to $$ \frac{1}{500} $$.

2. **Multiply the fractions**:
   $$
   (0.2) \cdot (0.002) = \left(\frac{1}{5}\right) \cdot \left(\frac{1}{500}\right)
   $$
   When multiplying fractions, you multiply the numerators together and the denominators together:
   $$
   = \frac{1 \cdot 1}{5 \cdot 500} = \frac{1}{2500}
   $$

3. **Convert the result back to a decimal**:
   To convert $$ \frac{1}{2500} $$ to a decimal, you can perform the division:
   $$
   1 \div 2500 = 0.0004
   $$

Thus, we have shown that:
$$
(0.2) \cdot (0.002) = 0.0004
$$

This confirms that the multiplication of the two decimals indeed results in $$ 0.0004 $$.
$$ 0.2 \times 0.002 = 0.0004 $$

tyou know about decimals or fractions to explain why

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