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

To understand why \( (0.2) \cdot (0.002) = 0.0004 \), let’s break it down a bit. First, convert both numbers into fractions: \( 0.2 = \frac{2}{10} \) and \( 0.002 = \frac{2}{1000} \). When you multiply them together, it’s \( \frac{2}{10} \cdot \frac{2}{1000} = \frac{4}{10000} \). Now, converting \( \frac{4}{10000} \) back to decimal form gives you \( 0.0004 \)! Next, let’s visualize the multiplication. Think of it as scaling the values down. When you multiply \( 0.2 \) (which is two-tenths) by \( 0.002 \) (which is two-thousandths), you are reducing their sizes, leading to a smaller product. Each decimal point you move represents a division by ten, so you end up moving the decimal four places to the left, resulting in \( 0.0004 \). Fun, right?