Question

What is the expanded form of 8,471.716?

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

(8×10 to the power of 3)+(4×10 to the power of 2)+(7×10 to the power of 1)+(1×10 to the power of 0)+(7×1/ 10 to the power od 1)+(1×1/10 to the power of 2)+(6×1/10 to the power of 3)

(8×1,000)+(4×100)+(7×10)+(1×1)+(7×11)+(1×110)+(6×1/100)

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

Answer 1

The expanded form of the number 8,471.716 can be expressed using both multiplication and powers of ten. Let's break it down:

1. The whole number part:
- 8,000 (which is 8 × 1,000)
- 400 (which is 4 × 100)
- 70 (which is 7 × 10)
- 1 (which is 1 × 1)

2. The decimal part:
- 0.7 (which is 7 × 1/10)
- 0.01 (which is 1 × 1/100)
- 0.006 (which is 6 × 1/1,000)

Putting it all together, the correct expanded form can be represented as:

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

This is equivalent to the second option you provided, which also uses powers of ten:

(8 × 10^3) + (4 × 10^2) + (7 × 10^1) + (1 × 10^0) + (7 × 10^-1) + (1 × 10^-2) + (6 × 10^-3)

From the options you listed, the first one and the second one accurately represent the expanded form of 8,471.716. Therefore, the correct answer is:

**(8×1,000)+(4×100)+(7×10)+(1×1)+(7×1/10)+(1×1/100)+(6×1/1,000)**
**and**
**(8×10 to the power of 3)+(4×10 to the power of 2)+(7×10 to the power of 1)+(1×10 to the power of 0)+(7×1/ 10 to the power of 1)+(1×1/10 to the power of 2)+(6×1/10 to the power of 3)**.