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

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 \( 0.0004 \).