Question

The mass of Earth is `5.9*10^24` kg. The mass is 13,000,000,000,000,000,000,000 kg. Compared to Pluto, how much greater is Earth's mass than Pluto's mass?

Answer 1

`5.887 * 10^24kg`.

Explanation:

convert the mass of pluto to standard form:

`13,000,000,000,000,000,000,000` is `13` with `21` zeroes.

this means that it is `21` places ahead of `13`.

`13` is `1` place ahead of `1.3`.

this means that `13,000,000,000,000,000,000,000` is `22` places ahead of `1.3`

the power of `10` that `1.3` is multiplied by to make `13,000,000,000,000,000,000,000` is the number of places ahead that `13,000,000,000,000,000,000,000` is from `1.3`

it is `22` places ahead, so `13,000,000,000,000,000,000,000 = 1.3 * 10^22`.

the mass of pluto is approximately `1.3 * 10^22kg`.

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it is given that the mass of earth is `5.9 * 10^24 kg`.

to find the difference between earth and pluto's mass, it may be easier to convert earth's mass into a multiple of `10^22`.

`5.9 * 10^24 = 5.9 * 10^2 * 10*22 = 590 * 10^22`

mass of earth: `590 * 10^22kg`
mass of pluto: `1.3 * 10^22kg`

`(590*10^22) - (1.3*10^22) = 588.7`

`588.7 * 10^22 = 5.887 * 10^24`

the difference between the masses of earth and pluto is `5.887 * 10^24kg`.