Answer the question.
-The distance from the Earth to the Sun is about $1.5 \times 10 ^ { 8 } \mathrm {~km}$, while the distance from the Earth to the moon is about $3.8 \times 10 ^ { 5 } \mathrm {~km}$. If a scale model of the solar system is constructed so that the distance from the Earth to the Sun is 100 meters, what will be the distance from the Earth to the moon?
A) $6.36 \mathrm {~m}$
B) $0.25 \mathrm {~m}$
C) $39.5 \mathrm {~m}$
D) $39,474 \mathrm {~m}$

Question

Quizplus · Accepted Answer

To find the scale distance from the Earth to the Moon, use the ratio of the actual distances. The actual distance to the Sun is $1.5 \times 10^8 $ km, represented by 100 meters in the model. Therefore, $1.5 \times 10^8 $ km corresponds to 100 meters, so $3.8 \times 10^5 $ km (the distance to the Moon) would correspond to $(3.8 \times 10^5 / 1.5 \times 10^8) \times 100 = 0.2533$ meters, which rounds to approximately 0.25 meters.

Answer the Question 1.5×108 km1.5 \times 10 ^ { 8 } \mathrm {~km}1.5×108 km

Answer the Question $1.5 \times 10 ^ { 8 } \mathrm {~km}$