To express the number 8,471.716 in expanded form, we will break down each digit according to its place value.
For the number 8,471.716:
- The digit 8 is in the thousands place, so it represents \(8 \times 1,000\)
- The digit 4 is in the hundreds place, so it represents \(4 \times 100\)
- The digit 7 is in the tens place, so it represents \(7 \times 10\)
- The digit 1 is in the ones place, so it represents \(1 \times 1\)
- The digit 7 is in the tenths place, so it represents \(7 \times \frac{1}{10}\)
- The digit 1 is in the hundredths place, so it represents \(1 \times \frac{1}{100}\)
- The digit 6 is in the thousandths place, so it represents \(6 \times \frac{1}{1000}\)
Now, putting it all together, the expanded form of 8,471.716 is:
\[ (8 \times 1,000) + (4 \times 100) + (7 \times 10) + (1 \times 1) + (7 \times \frac{1}{10}) + (1 \times \frac{1}{100}) + (6 \times \frac{1}{1,000}) \]
So the correct option for the expanded form of 8,471.716 from your provided choices is:
\[ (8 \times 1,000) + (4 \times 100) + (7 \times 10) + (1 \times 1) + (7 \times \frac{1}{10}) + (1 \times \frac{1}{100}) + (6 \times \frac{1}{1,000}) \]