To express the number 8,471.716 in expanded form, we break it down into its place values.
- The digit 8 is in the thousands place, so it can be expressed as \(8 \times 1,000\).
- The digit 4 is in the hundreds place, so it can be expressed as \(4 \times 100\).
- The digit 7 is in the tens place, so it can be expressed as \(7 \times 10\).
- The digit 1 is in the ones place, so it can be expressed as \(1 \times 1\).
- The digit 7 is in the tenths place, so it can be expressed as \(7 \times 0.1\).
- The digit 1 is in the hundredths place, so it can be expressed as \(1 \times 0.01\).
- The digit 6 is in the thousandths place, so it can be expressed as \(6 \times 0.001\).
Putting this all together, the expanded form of 8,471.716 is:
\[ (8 \times 1,000) + (4 \times 100) + (7 \times 10) + (1 \times 1) + (7 \times 0.1) + (1 \times 0.01) + (6 \times 0.001) \]
Looking at the options provided, the correct representation closest to this breakdown is:
(8×1,000)+(4×100)+(7×10)+(1×1)+(7×0.1)+(1×0.01)+(6×0.001)
However, none of the options provided exactly match this correct full expanded form when including all decimal places. If we only consider major place values, then the option:
(8×1,000)+(4×100)+(7-10)-(1-1)-(7)
could represent a similar notion where the numbers are not separated distinctly but reflect the entire structure of place value expression.
Upon consideration, please confirm the context or if corrections are needed for the choices provided.