# Just because a number is a rounding error doesn't mean it's not important

Sometimes, people call a number a “rounding error” as if to say it doesn’t matter. But a rounding error can still be very important!

Say I’m tracking my weight. If I’ve put on 0.1 pounds since yesterday, that’s a rounding error—my weight fluctuates by 3 pounds on a day-to-day basis, so 0.1 pounds means nothing. But if I continue gaining 0.1 pounds per day, I’ll be obese after 18 months, and by the time I’m 70 I’ll be the fattest person who ever lived.

Or if the stock market moves 1% in a day, that’s a rounding error. If it moves up 1% every day for a year, every individual day of which is a rounding error, it will be up 3700%, which would be the craziest thing that’s ever happened in the history of the global economy.

This happens whenever the standard deviation is much larger than the mean. A large standard deviation means a “real” change gets obscured by random movement. But over enough iterations, the random movements even out and the real changes persist. For example, the stock market has an average daily return of 0.02% and a standard deviation of 0.8%. The standard deviation is 40x larger than the mean, so a real trend in prices gets totally washed out by noise. The market’s daily average return is a rounding error, but it’s still important.