Concept explainers
The diameter of the moon is approximately 3.5×103 kilometres.
a. The diameter of Earth is approximately 3.7 times the diameter of the moon. Determine the diameter of Earth. Write your answer in scientific notation.
b. The distance from the centre of Earth to the centre of the moon is approximately 30 times the diameter of Earth. Determine the distance from the centre of Earth to the centre of the moon. Write your answer in scientific notation.
a.

Tocalculate : The diameter of Earth in scientific notation
Answer to Problem 43P
Diameter of Earth =1.295×104 kilometre
Explanation of Solution
Given information : The diameter of the moon is approximately 3.5×103 kilometre and the diameter of Earth is approximately 3.7 times the diameter of the moon
Calculation :
Diameter of moon =3.5×103 kilometre
Diameter of Earth =3.7× Diameter of the moon
So,
Diameter of Earth =3.7×3.5×103=12.95×103 kilometre
In scientific notation, 12.95×103 can be written as 12.95×103=1.295×104
(A number is said to be in scientific notation if it lies between 1 and 10 and it is multiplied by a power of 10.)
Hence,
Diameter of Earth =1.295×104 kilometre
b.

Tocalculate : Distance from the center of the Earth to the center of the moon
Answer to Problem 43P
Distance from the center of the Earth to the center of the moon =3.885×105 kilometre
Explanation of Solution
Calculation :
Diameter of Earth =1.295×104 kilometre
Distance from the center of the Earth to the center of the moon =30× Diameter of the Earth
So,
Distance from the center of the Earth to the center of the moon =30×1.295×104=3885×102 kilometre
In scientific notation,
Distance from the center of the Earth to the center of the moon =3885×102=3.885×105 kilometre
(A number is said to be in scientific notation if it lies between 1 and 10 and it is multiplied by a power of 10.)
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