Question

What is the expanded form of 8,471.716?

options:

(8 × 10^3) + (4 × 10^2)+(7 × 10^1) + (7×1 over 10^1) + (1 × 1 over 10^2)+(6 × 1 over 103^)

(8 × 1,000) + (4 × 100) + (7 × 10) + (1 × 1) + (7 ×1 over 10) + (1 × 1 over 100) + (6 × 1 over 1,000)

(8 × 1,000) + (4 × 100) + (7 × 10) + (1 × 1) + (7 × 1 over 10) + (1 × 1 over 10) + (6 × 1 over 100)

(8 × 1,000) + (4 × 100) + (7 × 10) + (1 × 1) + (7 × 1 over 10) + (1 × 1 over 100)

Answer 1

To express the number 8,471.716 in expanded form, we break it down by each digit's place value:

- 8,000 (8 in the thousands place)
- 400 (4 in the hundreds place)
- 70 (7 in the tens place)
- 1 (1 in the ones place)
- 0.7 (7 in the tenths place, which is 7/10)
- 0.01 (1 in the hundredths place, which is 1/100)
- 0.006 (6 in the thousandths place, which is 6/1000)

Combining these gives us:

(8 × 1,000) + (4 × 100) + (7 × 10) + (1 × 1) + (7 × 1/10) + (1 × 1/100) + (6 × 1/1,000)

Now, let's compare this with the provided options:

1. (8 × 10^3) + (4 × 10^2)+(7 × 10^1) + (7×1 over 10^1) + (1 × 1 over 10^2)+(6 × 1 over 10^3)
2. (8 × 1,000) + (4 × 100) + (7 × 10) + (1 × 1) + (7 ×1 over 10) + (1 × 1 over 100) + (6 × 1 over 1,000)
3. (8 × 1,000) + (4 × 100) + (7 × 10) + (1 × 1) + (7 × 1 over 10) + (1 × 1 over 10) + (6 × 1 over 100)
4. (8 × 1,000) + (4 × 100) + (7 × 10) + (1 × 1) + (7 × 1 over 10) + (1 × 1 over 100)

The correct expanded form of 8,471.716 aligns with option 2, as it correctly includes the terms for all the decimal places.

So the answer is:

**(8 × 1,000) + (4 × 100) + (7 × 10) + (1 × 1) + (7 × 1 over 10) + (1 × 1 over 100) + (6 × 1 over 1,000)**