To arrange the numbers \(0.733\), \(0.923\), \(1 \frac{2}{5}\), \(\frac{17}{20}\), and \(\frac{15}{18}\) in descending order, we first need to convert everything into decimal form.
- \(0.733\) is already in decimal form.
- \(0.923\) is also in decimal form.
- \(1 \frac{2}{5} = 1 + \frac{2}{5} = 1 + 0.4 = 1.4\).
- \(\frac{17}{20} = 0.85\) (since \(17 \div 20 = 0.85\)).
- \(\frac{15}{18} = 0.8333\) (since \(15 \div 18 \approx 0.8333\)).
Now, listing them all in decimal form:
- \(0.733\)
- \(0.923\)
- \(1.4\)
- \(0.85\)
- \(0.8333\)
Next, we arrange these decimals in descending order:
- \(1.4\)
- \(0.923\)
- \(0.85\)
- \(0.8333\)
- \(0.733\)
So, the fractions and decimals in descending numerical order are:
\[ 1 \frac{2}{5}, 0.923, \frac{17}{20}, \frac{15}{18}, 0.733 \]