# Why does $e$ seem to be an intuitive number? [closed]

I often find two numbers roughly "in the same ballpark" if they are within a factor of about $e$ of each other. For example, if I know computers generally cost upward of $\$1000$, then$\$2700$ would probably be the most I would a priori feel is a reasonable upper limit for computer prices.

Is this just a coincidence, or is there some mathematical deep reason why $e$ is inherently the "best" order-of-magnitude exponent?

## closed as off-topic by Antonio Vargas, Dan Rust, Norbert, Dominic Michaelis, user61527 Nov 7 '13 at 19:46

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is not about mathematics, within the scope defined in the help center." – Antonio Vargas, Dan Rust, Norbert, Dominic Michaelis, Community
If this question can be reworded to fit the rules in the help center, please edit the question.

• Interesting observation. – Lord Soth Nov 7 '13 at 17:48
• That is a subjective assessment. Different people have different notions of close or not close. It is easier in certain math operations though. – user76844 Nov 7 '13 at 17:49
• $e$ is an amazing number and pops up a lot of places. – MasterOfBinary Nov 7 '13 at 17:58

• @user54609 Because $\log_{10} \sqrt{10} = 0.5$, i.e., half way on the logarithmic scale. – zrbecker Nov 7 '13 at 18:27