The expanded form of the number 8,471.716 can be broken down into its place values.
- The digit '8' is in the thousands place, so it is represented by \(8 \times 1,000\).
- The digit '4' is in the hundreds place, so it is represented by \(4 \times 100\).
- The digit '7' is in the tens place, so it is represented by \(7 \times 10\).
- The digit '1' is in the units place (ones), so it is represented by \(1 \times 1\).
- The digit '7' in the tenths place can be represented as \(7 \times \frac{1}{10}\).
- The digit '1' in the hundredths place can be represented as \(1 \times \frac{1}{100}\).
- The digit '6' in the thousandths place can be represented as \(6 \times \frac{1}{1000}\).
So, the correct expanded form is:
\[ (8 \times 1,000) + (4 \times 100) + (7 \times 10) + (1 \times 1) + (7 \times \frac{1}{10}) + (1 \times \frac{1}{100}) + (6 \times \frac{1}{1000}) \]
Thus, the appropriate response is:
(8×1,000)+(4×100)+(7×10)+(1×1)+(7×(1/10))+(1×(1/100))+(6×(1/1000))