Question

The approximate distance of the moon from Earth is 4 x 10 5
km and the average approximate distance from the Earth to Venus is 4 x 10 7
km. How much farther is Venus from Earth than the moon?
Responses
A 10 times farther10 times farther
B 100 times farther100 times farther
C 1000 times farther1000 times farther
D about the same distanceabout the same distance
E



1/100 times farther

Answer 1

To find out how much farther Venus is from Earth than the Moon, we can subtract the distance of the Moon from the distance of Venus:

1. Distance of the Moon from Earth: \(4 \times 10^5\) km
2. Distance of Venus from Earth: \(4 \times 10^7\) km

To find the difference:

\[
4 \times 10^7 \text{ km} - 4 \times 10^5 \text{ km} \approx 4 \times 10^7 \text{ km} \quad (\text{since } 4 \times 10^5 \text{ is negligible compared to } 4 \times 10^7)
\]

Now, we can determine how many times farther Venus is from Earth than the Moon:

\[
\frac{4 \times 10^7 \text{ km}}{4 \times 10^5 \text{ km}} = \frac{4}{4} \times \frac{10^7}{10^5} = 1 \times 10^{2} = 100
\]

So, Venus is approximately **100 times farther** from Earth than the Moon.

The correct response is:

**B 100 times farther**