To express the number 8,471.716 in expanded form, we break it down based on the place value of each digit.
The expanded form of 8,471.716 would be:
- 8 in the thousands place: \( 8 \times 1,000 \)
- 4 in the hundreds place: \( 4 \times 100 \)
- 7 in the tens place: \( 7 \times 10 \)
- 1 in the ones (units) place: \( 1 \times 1 \)
- 7 in the tenths place: \( 7 \times \frac{1}{10} \)
- 1 in the hundredths place: \( 1 \times \frac{1}{100} \)
- 6 in the thousandths place: \( 6 \times \frac{1}{1,000} \)
Putting this all together, the correct expanded form is:
\((8 \times 1,000) + (4 \times 100) + (7 \times 10) + (1 \times 1) + (7 \times \frac{1}{10}) + (1 \times \frac{1}{100}) + (6 \times \frac{1}{1,000})\)
So the matching response is:
(8×1,000)+(4×100)+(7×10)+(1×1)+(7×(1/10))+(1×(1/100))+(6×(1/1,000)).