What makes the inequality true? \[ \frac{2}{5}<\text { ? } \] \( \frac{1}{6} \) 0.13 \( \sqrt{0.5} \)

To determine what makes the inequality \( \frac{2}{5} < \text{ ? } \) true, let's evaluate the candidates. First, \( \frac{2}{5} = 0.4 \). The fraction \( \frac{1}{6} \) is approximately 0.1667, which is less than 0.4, making it a contender! Next, 0.13 is even smaller and definitely less than 0.4. Finally, \( \sqrt{0.5} \) is about 0.7071, which is greater than 0.4. So, the inequality holds true for both \( \frac{1}{6} \) and 0.13, but not for \( \sqrt{0.5} \). Choosing between multiple options can be tricky, especially if you're not carefully comparing their values! A common mistake is overlooking how decimal approximations compare to fractions. To avoid this, always convert everything to the same format (either all decimals or all fractions) when making comparisons. This way, it's way easier to see which numbers are smaller or larger!