To find the expanded form of 8,471.716, we can break it down into its place values:
- The digit 8 is in the thousands place: \(8 \times 1,000\)
- The digit 4 is in the hundreds place: \(4 \times 100\)
- The digit 7 is in the tens place: \(7 \times 10\)
- The digit 1 is in the ones place: \(1 \times 1\)
- The digit 7 is in the tenths place: \(7 \times \frac{1}{10}\)
- The digit 1 is in the hundredths place: \(1 \times \frac{1}{100}\)
- The digit 6 is in the thousandths place: \(6 \times \frac{1}{1,000}\)
Putting it all together, the expanded form of 8,471.716 is:
\[ (8 \times 1,000) + (4 \times 100) + (7 \times 10) + (1 \times 1) + (7 \times \frac{1}{10}) + (1 \times \frac{1}{100}) + (6 \times \frac{1}{1,000}) \]
This matches the third choice from your options: \((8 \times 1,000) + (4 \times 100) + (7 \times 10) + (1 \times 1) + (7 \times \frac{1}{10}) + (1 \times \frac{1}{100}) + (6 \times \frac{1}{1,000})\).
So the correct response is:
(8×1,000) + (4×100) + (7×10) + (1×1) + (7×(1/10)) + (1×(1/100)) + (6×(1/1,000))