I’m using approximate powers-of-ten here to make the mental arithmetic easier. The actual numbers are less neat. When dealing with very large or very small numbers it’s important to get the number of zeros right quickly, and only then sweat the details. Precise, unwieldy numbers usually don’t help in the early stages of analysis.
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Facebook engineer shares interesting hints on estimating scalability of the architecture. Also, illustrates well the power of the bottom-up understanding of the system.