The mass of the earth is 5,976,000,000,000,000,000,000,000 Kg and the radius of the earth is 6.37 x 106m. Moon is the natural satellite of earth which revolves around the sun due to strong gravitational force of the earth. The mass of the moon is 7.36 x 10 raised to 22Kg. The radius of the moon is 1.74 x 10 raised to 6 m. The distance between the earth and moon is 3.84 x 10 raised to 5 km.(AO2)a. Write the mass of earth in standard form?b. Express the distance between earth and moon in m and find its square. Write your answer in standard form?c. Express the double of difference of radius of earth and moon in standard form

Q1: The correct answer is: $5.976\times10^{24}\text{ kg}$

Explanation

Steps:

1. Write the given mass: $$5,976,000,000,000,000,000,000,000\text{ kg}$$
2. Move the decimal after the first nonzero digit to get standard form: $$5,976,000,000,000,000,000,000,000=5.976\times10^{24}\text{ kg}$$

Q2: The correct answer is: distance $=3.84\times10^{8}\text{ m}$; square $=1.47456\times10^{17}\text{ m}^2$

Explanation

Steps:

1. Convert km to m: $$3.84\times10^{5}\text{ km}=3.84\times10^{5}\times10^{3}\text{ m}=3.84\times10^{8}\text{ m}$$
2. Square the distance: $$(3.84\times10^{8})^{2}=3.84^{2}\times10^{16}=14.7456\times10^{16}=1.47456\times10^{17}\text{ m}^2$$

Q3: The correct answer is: $9.26\times10^{6}\text{ m}$

Explanation

Steps:

1. Difference of radii: $$6.37\times10^{6}\text{ m}-1.74\times10^{6}\text{ m}=(6.37-1.74)\times10^{6}=4.63\times10^{6}\text{ m}$$
2. Double that difference: $$2\times4.63\times10^{6}=9.26\times10^{6}\text{ m}$$

If you want, I can also give these answers rounded to a different number of significant figures.