To express the number 8,471.716 in expanded form, we break it down according to the place value of each digit. The expanded form is shown by multiplying each digit by its place value.
For the entire number 8,471.716:
- The digit "8" is in the thousands place: 8 × 1,000
- The digit "4" is in the hundreds place: 4 × 100
- The digit "7" is in the tens place: 7 × 10
- The digit "1" is in the ones place: 1 × 1
- The digit "7" in the tenths place: 7 × 0.1 (which is 7/10)
- The digit "1" in the hundredths place: 1 × 0.01 (which is 1/100)
- The digit "6" in the thousandths place: 6 × 0.001 (which is 6/1000)
Putting this all together, we can express 8,471.716 as: (8 × 1,000) + (4 × 100) + (7 × 10) + (1 × 1) + (7 × 1/10) + (1 × 1/100) + (6 × 1/1,000)
Therefore, the correct expanded form is:
(8×1,000)+(4×100)+(7×10)+(1×1)+(7×1/10)+(1×1/100)+(6×1/1,000)
Among the provided responses, the closest representation is:
left parenthesis 8 times 1,000 right parenthesis plus left parenthesis 4 times 100 right parenthesis plus left parenthesis 7 times 10 right parenthesis plus left parenthesis 1 times 1 right parenthesis plus left parenthesis 7 times Start Fraction 1 over 10 End Fraction right parenthesis plus left parenthesis 1 times Start Fraction 1 over 100 End Fraction right parenthesis plus left parenthesis 6 times Start Fraction 1 over 1,000 End Fraction right parenthesis