1 The volume of a number cube is \( 27 \mathrm{~cm}^{3} \). What is the length of each side of the cube? (B) 6 cm (C) 9 cm (D) 81 cm 2 Which decimal is equivalent to \( \frac{8}{9} \) ? (A) \( 0 . \overline{8} \) (b) 0.88 (C) \( 0.8 \overline{9} \) (D) 0.9 3 Between which two consecutive integers is \( \frac{\sqrt{40}}{2} \) ? \( \qquad \) and \( \qquad \) -

To find the length of each side of the cube with a volume of \( 27 \text{ cm}^3 \), you need to take the cube root of the volume. The cube root of \( 27 \) is \( 3 \), so the length of each side is \( 3 \text{ cm} \). Oops! The catch here is that the options provided do not include the correct answer, which illustrates that sometimes multiple-choice questions can be tricky! When considering the decimal equivalent of \( \frac{8}{9} \), it is \( 0.888... \), often expressed as \( 0.\overline{8} \). This means that the digit \( 8 \) repeats indefinitely, making it an interesting case in decimal notation. If you're up for exploring, it’s fascinating how similar fractions can have very different decimal representations! To estimate \( \frac{\sqrt{40}}{2} \), you first need to simplify \( \sqrt{40} \), which is about \( 6.32 \). Dividing by \( 2 \) gives approximately \( 3.16 \). Hence, it falls between the consecutive integers \( 3 \) and \( 4 \). You can visualize this with a number line - it's like strolling along where each step represents an integer!