Math for coding interviews/Orders of magnitude - powers of 10
Orders of Magnitude: Powers of 10, Visualized
Each "order of magnitude" is 10x bigger. A system handling 1,000 requests/second versus 100,000 requests/second is two orders of magnitude different - not 100 units, but 100x. System design constantly compares numbers at different orders of magnitude.
See it for yourself
A number line that is exponential, not linear. Each tick mark is 10x bigger than the previous. 1, 10, 100, 1,000, 10,000, 100,000, 1,000,000. The visual distance between 1 and 10 looks the same as between 1,000 and 10,000.
Orders of magnitude - powers of 10
Each "order of magnitude" is 10x bigger. A system handling 1,000 requests/second versus 100,000 requests/second is two orders of magnitude different - not 100 units, but 100x. System design constantly compares numbers at different orders of magnitude.
Think of it this way: The difference between a lemonade stand and a restaurant and a fast food chain and a global food company. Same product, but each order of magnitude in scale requires fundamentally different systems.
For algorithms: System design interviewers often test whether you can reason about scale. "Handle 10 million users" means understanding what changes at each order of magnitude, not just adding more servers.
Real-world analogy
The difference between a lemonade stand and a restaurant and a fast food chain and a global food company. Same product, but each order of magnitude in scale requires fundamentally different systems.
Why it matters in interviews
System design interviewers often test whether you can reason about scale. "Handle 10 million users" means understanding what changes at each order of magnitude, not just adding more servers.