Question 3 \( 3.1 \quad \) Arrange the following numbers in the ascending order \( { }_{3} \) \[ 9,-4, \frac{1}{10}, 0, \sqrt[3]{8}, \pi \]

To arrange the numbers in ascending order in base \(3\), we first need to convert all the numbers to decimal for better comparisons, but it’s important to note how these values appear in base \(3\). The numbers converted to decimal are: - \(9\) - \(-4\) (which is already negative) - \(\frac{1}{10} = 0.1\) (approximately) - \(0\) - \(\sqrt[3]{8} = 2\) - \(\pi \approx 3.14\) Now, let's rank them: - The smallest is \(-4\) - Next is \(0\) - Followed by \(\frac{1}{10}\) (approximately \(0.1\)) - Then we have \(2\) - After that, \(\pi\) (approximately \(3.14\)) - Finally, \(9\) Now, if we convert these decimal results to base \(3\): - \(-4\) is \(-11\) in base \(3\) - \(0\) is \(0\) in base \(3\) - \(0.1\) can't be expressed precisely but is very little, still close to \(0\) in base \(3\) - \(2\) is \(2\) in base \(3\) - \(\pi \approx 3.14 \approx 10\) in base \(3\) - \(9\) is \(100\) in base \(3\) So the ascending order in base \(3\) is: \[ -4, 0, \frac{1}{10}, 2, \pi, 9 \]