(a) Write the numbers \( 0.017,0.007,0.01 \overline{7}, 0.027 \) in order from least to greatest. \( \square \nabla \square \)

To compare the numbers \( 0.017, 0.007, 0.01 \overline{7}, 0.027 \), we will first convert \( 0.01 \overline{7} \) into a fraction for easier comparison. 1. **Convert \( 0.01 \overline{7} \) to a fraction:** Let \( x = 0.01 \overline{7} \). Then, \( 100x = 1.7 \overline{7} \). Subtracting the first equation from the second gives: \[ 100x - x = 1.7 \overline{7} - 0.01 \overline{7} \] \[ 99x = 1.69 \] \[ x = \frac{1.69}{99} \] To convert \( 1.69 \) to a fraction: \[ 1.69 = \frac{169}{100} \] Thus, \[ x = \frac{169}{100 \times 99} = \frac{169}{9900} \] 2. **Convert all numbers to decimals for comparison:** - \( 0.007 \) is already in decimal form. - \( 0.017 \) is already in decimal form. - \( 0.01 \overline{7} \) is approximately \( 0.017 \) (as calculated). - \( 0.027 \) is already in decimal form. 3. **List the numbers:** - \( 0.007 \) - \( 0.017 \) - \( 0.01 \overline{7} \approx 0.017 \) - \( 0.027 \) 4. **Order from least to greatest:** - \( 0.007 \) - \( 0.017 \) - \( 0.01 \overline{7} \) - \( 0.027 \) Thus, the final order from least to greatest is: \[ 0.007, 0.017, 0.01 \overline{7}, 0.027 \]