Today a student asked me, "Can you write the number zero in scientific notation?" This got me thinking.
As a refresher, when we write a number $x$ in scientific notation, we write $x$ as
$$x = a\cdot 10^n$$
where $1\le |a| < 10$ is a real number and $n$ is an integer. We can do this uniquely for any number we like.
Except zero. The student had recognized that if we want to write $0$ in scientific notation as $0=a\cdot 10^n$, then $a$ has to equal $0$, violating the inequality above, and also $n$ could be any number (shifting the decimal place on $0.00$ doesn't change the number). She saw that we're stuck with expending the concept of scientific notation in a messy way or with leaving $0$ as the oddball out. How do you think we should resolve this?
I started this blog to share my transformation from math nerd to math nerd who loves to share math with young people. I teach high school in Hanoi, Vietnam. Your comments are always welcome.