To arrange the given fractions and decimals in ascending numerical order, we can convert them all into decimal form for easier comparison:
- \( \frac{2}{3} = 0.6667 \) (approximately)
- \( \frac{7}{9} = 0.7777 \) (approximately)
- \( 0.8 \)
- \( 0.833 \)
- \( 0.857 \)
Now we can list them in decimal order:
- \( \frac{2}{3} \approx 0.6667 \)
- \( \frac{7}{9} \approx 0.7777 \)
- \( 0.8 \)
- \( 0.833 \)
- \( 0.857 \)
So, the ascending order of the fractions and decimals is:
\[ \frac{2}{3}, \frac{7}{9}, 0.8, 0.833, 0.857 \]