Chapter 7.2, Problem 43P

The diameter of the moon is approximately $3.5\times {10}^3$ 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.

To determine

Tocalculate : The diameter of Earth in scientific notation

Answer to Problem 43P

Diameter of Earth $=1.295\times {10}^4$ kilometre

Explanation of Solution

Given information : The diameter of the moon is approximately $3.5\times {10}^3$ kilometre and the diameter of Earth is approximately $3.7$ times the diameter of the moon

Calculation :

Diameter of moon $=3.5\times {10}^3$ kilometre

Diameter of Earth $=3.7\times$ Diameter of the moon

So,

Diameter of Earth $=3.7\times 3.5\times {10}^3=12.95\times {10}^3$ kilometre

In scientific notation, $12.95\times {10}^3$ can be written as $12.95\times {10}^3=1.295\times {10}^4$

(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 $=1.295\times {10}^4$ kilometre

To determine

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 $=3.885\times {10}^5$ kilometre

Explanation of Solution

Calculation :

Diameter of Earth $=1.295\times {10}^4$ kilometre

Distance from the center of the Earth to the center of the moon $=30\times$ Diameter of the Earth

So,

Distance from the center of the Earth to the center of the moon $=30\times 1.295\times {10}^4=3885\times {10}^2$ kilometre

In scientific notation,

Distance from the center of the Earth to the center of the moon $=3885\times {10}^2=3.885\times {10}^5$ 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.)