# Order of magnitude of zero?

I was wondering what exactly the order of magnitude is of 0. Just by calculating it you obviously get $$-\infty$$ because of the logarithm but is this really correct?

## 2 Answers

Yes the order of magnitude of zero is $$-\infty$$. For increasingly small values (like $$10^{-3}$$, $$10^{-31}$$, $$10^{-314}$$, $$10^{-3141}$$ and so on), you can see it approaches larger and larger negative values. As you get closer and closer to zero, the order of magnitude gets more and more larger negative value, until you hit zero, when the order of magnitude blows down to $$-\infty$$. Strictly speaking, order of magnitude of zero is not defined, however it's sometimes said to have a magnitude of $$-\infty$$. This infinitely negative order of magnitude indicates that zero is smaller than any other positive number, and so is its order of magnitude.

Order of magnitude of zero is not defined.

In mathematical form: $$0=\lim_{x\to -\infty}10^{x}$$ Above expression shows that the order of magnitude of zero tends to be $$-\infty$$

• This is wrong. The scientific notation of a number is of the form: $a\times 10^b$, where $10> a\geq1$. Thus you can't put $a$ as $0$. – user258881 May 1 at 7:42