C.2. Which list shows these rational numbers ordered from least to greatest? A. \( 0.03,0 . \overline{3}, 0.3 \) B. \( 0.03,0 . \overline{3}, 0.3 \) C. \( 0.3,0 . \overline{3}, 0.03 \) D. \( 0.3,0.03,0.3 \)

To compare the given decimal numbers, let's convert each of them for clarity: \( 0.03 \) is simply \( 0.03 \), \( 0.\overline{3} \) equals \( \frac{1}{3} \) or approximately \( 0.333... \), and \( 0.3 \) remains \( 0.3 \). Now, putting them in order, we have \( 0.03 < 0.3 < 0.333... \). So, the correct ordering from least to greatest is \( 0.03, 0.3, 0.\overline{3} \). If you've ever struggled with understanding repeating decimals, you're not alone! A neat trick is to convert them into fractions. For example, \( 0.\overline{3} \) can be calculated by letting \( x = 0.\overline{3} \), then multiplying by 10 gives \( 10x = 3.\overline{3} \). Subtracting the original equation leads to \( 9x = 3 \), so \( x = \frac{1}{3} \). It makes comparisons a breeze!