The expanded form of the number 8,471.716 can be expressed using its place values.
Let's break it down:
- The digit 8 is in the thousands place, so it represents 8 × 1,000.
- The digit 4 is in the hundreds place, so it represents 4 × 100.
- The digit 7 is in the tens place, so it represents 7 × 10.
- The digit 1 is in the ones (units) place, so it represents 1 × 1.
- The digit 7 in the tenths place (first digit after the decimal) represents 7 × (1/10) or 7 × 0.1.
- The digit 1 in the hundredths place represents 1 × (1/100) or 1 × 0.01.
- The digit 6 in the thousandths place represents 6 × (1/1000) or 6 × 0.001.
In written form, this gives us the expanded form:
\[ (8 \times 1,000) + (4 \times 100) + (7 \times 10) + (1 \times 1) + (7 \times \frac{1}{10}) + (1 \times \frac{1}{100}) + (6 \times \frac{1}{1000}) \]
Thus, the correct choice from your responses is:
(8×1,000)+(4×100)+(7×10)+(1×1)+(7×(1/10))+(1×(1/100))+(6×(1/1000)).