Hanif works out the range of \( 1 \frac{9}{10}, 3 \frac{7}{8}, 1 \frac{3}{4}, 2 \frac{3}{11} \) and 3 He writes \( 3 \frac{1}{3}-1 \frac{9}{10}=1 \frac{13}{20} \) He is wrong. Work out the correct range.

To find the range of the given numbers \(1 \frac{9}{10}\), \(3 \frac{7}{8}\), \(1 \frac{3}{4}\), \(2 \frac{3}{11}\), and \(3\), we first need to convert these mixed numbers into improper fractions or decimals for easy comparison. 1. Convert mixed numbers: - \(1 \frac{9}{10} = 1 + \frac{9}{10} = \frac{10}{10} + \frac{9}{10} = \frac{19}{10} = 1.9\) - \(3 \frac{7}{8} = 3 + \frac{7}{8} = \frac{24}{8} + \frac{7}{8} = \frac{31}{8} = 3.875\) - \(1 \frac{3}{4} = 1 + \frac{3}{4} = \frac{4}{4} + \frac{3}{4} = \frac{7}{4} = 1.75\) - \(2 \frac{3}{11} = 2 + \frac{3}{11} = \frac{22}{11} + \frac{3}{11} = \frac{25}{11} \approx 2.2727\) - \(3 = 3\) 2. Now, we arrange the numbers: - \(1.9, 1.75, 2.2727, 3, 3.875\) 3. Identify the minimum and maximum values: - Minimum = \(1.75\) (which is \(1 \frac{3}{4}\)) - Maximum = \(3.875\) (which is \(3 \frac{7}{8}\)) 4. Calculate the range: \[ \text{Range} = \text{Maximum} - \text{Minimum} = 3.875 - 1.75 = 2.125 \] So, the correct range is \(2.125\).