As an engineering student, I often use each of these methods. I consider each of these options a tool in my toolbox. I’ll often specifically choose one based on the problem I am attempting to solve and my intended audience. Here are a few observations I would add:
Scientific notation (3×104)
This can be converted to a standard number by any person that understands exponents and multiplication. As a result, it is still legible to any without a formal introduction to scientific notation, and for those who may lack the intuitive understanding of the need for scientific notation that comes from doing many calculations across orders of magnitude.
e notation (3e4)
If typesetting is lost on copy and paste, I have seen 3e4 and 3e4 both become 3e4. Using a capital or smallcaps e can help distinguish between the two.
Engineering notation (30e3)
Some calculations involve multiplying and dividing many constants and variables in series. If it is important to understand the meaning of each term on its own and how each term contributes to the overall result, engineering notation can make the calculation significantly easier to follow. Such calculations often occur in engineering, hence the name. Fermi approximations are also a good example. (https://en.wikipedia.org/wiki/Fermi_problem)
As an engineering student, I often use each of these methods. I consider each of these options a tool in my toolbox. I’ll often specifically choose one based on the problem I am attempting to solve and my intended audience. Here are a few observations I would add:
Scientific notation (3×104)
This can be converted to a standard number by any person that understands exponents and multiplication. As a result, it is still legible to any without a formal introduction to scientific notation, and for those who may lack the intuitive understanding of the need for scientific notation that comes from doing many calculations across orders of magnitude.
e notation (3e4)
If typesetting is lost on copy and paste, I have seen 3e4 and 3e4 both become 3e4. Using a capital or smallcaps e can help distinguish between the two.
Engineering notation (30e3)
Some calculations involve multiplying and dividing many constants and variables in series. If it is important to understand the meaning of each term on its own and how each term contributes to the overall result, engineering notation can make the calculation significantly easier to follow. Such calculations often occur in engineering, hence the name. Fermi approximations are also a good example. (https://en.wikipedia.org/wiki/Fermi_problem)