To arrange the fractions and decimals in ascending numerical order, let's first convert the fractions into decimals for easier comparison:
- \( \frac{7}{9} \approx 0.7777... \) (repeating)
- \( \frac{2}{3} = 0.6666... \) (repeating)
- \( 0.8 = 0.8 \)
- \( 0.857 = 0.857 \)
- \( 0.833 = 0.833 \)
Now, we have the following decimals to compare:
- \( 0.6666...\) (from \( \frac{2}{3} \))
- \( 0.7777...\) (from \( \frac{7}{9} \))
- \( 0.8 \)
- \( 0.833 \)
- \( 0.857 \)
Now, we can arrange them in ascending order:
- \( \frac{2}{3} \) (0.6666...)
- \( \frac{7}{9} \) (0.7777...)
- \( 0.8 \)
- \( 0.833 \)
- \( 0.857 \)
Thus, the ascending numerical order is:
\( \frac{2}{3}, \frac{7}{9}, 0.8, 0.833, 0.857 \)