Question

Mercury is 5.8×107
km from the sun. Neptune is 4.5×1010
km from the sun. How much further is Neptune from the sun than Mercury?(1 point)
Responses

Divide the distances: 4.5×10105.8×107=0.78×103 =7.8×102
km
Divide the distances: 4.5×10105.8×107=0.78×103 =7.8×102
km

Multiply the distances: (5.8×107)⋅(4.5×1010) = (5.8×4.5)⋅(107+10)=26.1×1017=2.61×1018
km
Multiply the distances: (5.8×107)⋅(4.5×1010) = (5.8×4.5)⋅(107+10)=26.1×1017=2.61×1018
km

Subtract the distances by getting the same power of 10: (4.5×1010)−(5.8×107) =(4.5×1010)−(0.0058×1010)=4.49×1010
km
Subtract the distances by getting the same power of 10: (4.5×1010)−(5.8×107) =(4.5×1010)−(0.0058×1010)=4.49×1010
km

Add the distances together: (5.8×107)+(4.5×1010) = 10.3×1017=1.03×1018
km

Answer 1

To find out how much further Neptune is from the Sun than Mercury, we need to subtract the distance of Mercury from the distance of Neptune.

Given:
- Distance of Neptune from the Sun: \( 4.5 \times 10^{10} \) km
- Distance of Mercury from the Sun: \( 5.8 \times 10^{7} \) km

We will adjust Mercury's distance to the same power of ten as Neptune's distance for easier subtraction.

1. Express \( 5.8 \times 10^{7} \) in terms of \( 10^{10} \):
\[
5.8 \times 10^{7} = 0.0058 \times 10^{10}
\]

2. Now, perform the subtraction:
\[
(4.5 \times 10^{10}) - (0.0058 \times 10^{10}) = (4.5 - 0.0058) \times 10^{10} = 4.4942 \times 10^{10} \text{ km}
\]

When rounded, it can be approximated as \( 4.49 \times 10^{10} \) km.

So, the correct response is:
**Subtract the distances by getting the same power of 10: \( (4.5 \times 10^{10}) - (5.8 \times 10^{7}) = 4.49 \times 10^{10} \) km.**