How do I read $1/3i$?

Question

In a mathematical textbook I found the expression $1/3i$. Should that be read as one divided by $3i$ or as one third of $i$?

Answer 1

Here's the rub: Matlab translates this is 1/(3i) whereas WolframAlpha says it's i/3. So pick your poison.

Answer 2

That’s a bad way to write, but if I have to choose in this case my standard interpretation is $1/3i=1/(3i)$ that is $$\frac1{3i}$$

indeed to express $(1/3)i$ one could write directly $i/3$ without any ambiguity.

Answer 3

Well it can be both:

• $$1/\left(3i\right)=\frac{1}{3i}=\frac{i}{3ii}=-\frac{i}{3}\tag1$$
• $$\left(1/3\right)i=\frac{1}{3}\cdot i\tag2$$

Answer 4

The notation $ 1/3i$ in your textbook is bad !

It can be both $\frac{1}{3}i$ and $\frac{1}{3i}$.