To arrange the given fractions and decimals in descending numerical order, we first need to convert them all to decimal form for comparison:
- \(0.733\) is already in decimal form.
- \(0.923\) is already in decimal form.
- For \(1 \frac{2}{5}\):
- Convert the mixed number to an improper fraction: \(1 \frac{2}{5} = \frac{5 \cdot 1 + 2}{5} = \frac{7}{5} = 1.4\).
- For \(\frac{17}{20}\):
- Convert to decimal: \(17 \div 20 = 0.85\).
- For \(\frac{15}{18}\):
- Convert to decimal: \(15 \div 18 \approx 0.8333\).
Now we have the following decimal equivalents:
- \(0.733\)
- \(0.923\)
- \(1.4\) (which is \(1 \frac{2}{5}\))
- \(0.85\) (which is \(\frac{17}{20}\))
- \(0.8333\) (which is \(\frac{15}{18}\))
Now let's arrange them in descending order:
- \(1.4\)
- \(0.923\)
- \(0.85\)
- \(0.8333\)
- \(0.733\)
Thus, the correct descending order is:
1 2/5, 0.923, 17/20, 15/18, 0.733.