The correct expanded form of the number 8,471.716 is represented as follows:
\[ (8 \times 1000) + (4 \times 100) + (7 \times 10) + (1 \times 1) + (7 \times \frac{1}{10}) + (1 \times \frac{1}{100}) + (6 \times \frac{1}{1000}) \]
This corresponds to the first option in your list.
To break it down:
- 8,000 is contributed by \( 8 \times 1000 \).
- 400 is contributed by \( 4 \times 100 \).
- 70 is contributed by \( 7 \times 10 \).
- 1 is contributed by \( 1 \times 1 \).
- 0.7 is contributed by \( 7 \times \frac{1}{10} \) (which is 0.7).
- 0.01 is contributed by \( 1 \times \frac{1}{100} \) (which is 0.01).
- 0.006 is contributed by \( 6 \times \frac{1}{1000} \) (which is 0.006).
Putting it all together gives you the number 8,471.716.