Popular estimate of the Earth's atmosphere possibly wrong?

[Dreksler]

TL;DR

My calculation says 5.1 quadrillion kg yet the frequently mentioned one says 5.1 quintillion kg.

So I just realized that on the internet the number that frequently pops up with regards to the total mass of the Earth's atmosphere is 5,100,000,000,000,000,000 kilograms. For example, the number is mentioned two times on the Wikipedia page for the Earth's atmosphere, there are more examples. Yet per square meter of surface, there is 100,000 pascals of pressure, which is 10,000 kilograms-force per meter square. The Earth's surface area is 510,000,000,000 meters. Multiplying 510,000,000,000 meters with 10,000 kilograms gets you the number of 5,100,000,000,000,000 kilograms and not the number of 5,100,000,000,000,000,000 kilograms, which is the number frequently mentioned. Am I missing something here?

 

[fresh_42]

Google says $5.15 \,\cdot\,10^{18}\text{ kg}.$

 

[Dreksler]

Google says $5.15 \,\cdot\,10^{18}\text{ kg}.$

I know, that is what I am questioning.

 

[fresh_42]

You seem to assume $10,000 \text{ kg}$ per square meter in accordance with the sources I saw. Then
\begin{align*}
4\pi \left(\dfrac{12,730,000\text{ m}}{2}\right)^2\cdot 10,000\text{ kg}\,\text{m}^{-2}=5,091,042,001,329,214,046.932\ldots \text{ kg}=5.1\cdot 10^{18}\text{ kg}
\end{align*}

 

[Dreksler]

You seem to assume $10,000 \text{ kg}$ per square meter in accordance with the sources I saw. Then
\begin{align*}
4\pi \left(\dfrac{12,730,000\text{ m}}{2}\right)^2\cdot 10,000\text{ kg}\,\text{m}^{-2}=5,091,042,001,329,214,046.932\ldots \text{ kg}=5.1\cdot 10^{18}\text{ kg}
\end{align*}

Multiplying 510,000,000,000 with 10,000 doesn't get you to the power of 15?

 

[fresh_42]

Multiplying 510,000,000,000 with 10,000 doesn't get you to the power of 15?

Sure, but I used an average radius for the Earth and got 510,000,000,000,000 square meters.

 

[Dreksler]

Sure, but I used an average radius for the Earth and got 510,000,000,000,000 square meters.

Okay, I get where I made the mistake now.