Calculator mode. ENG mode?? (SCI vs. FLO vs. ENG)

Question

When I type 8*6

FLO = 48

SCI = $4.8 * 10^1$

ENG = $48 * 10^0$

1) What is the point of ENG mode??

2) What are situations where you want answers in SCIentific notation?

Answer 1

Engineering mode expresses numbers in the form $a\cdot 10^n$ where $n$ is a multiple of $3$. This is well suited to mentally convert into SI unit prefixes (kilo, mega, giga, tera, etc. and milli, micro, nano, pico, etc.). If you do not have such conversions in mind, scientific notation is the nicest way to have an immediately visible size / order of magnitude. For numbers between $0.001$ and $9999$ I would certainly prefer FLO mode though.

Answer 2

Scientific and engineering mode are useful for very big and very small numbers. It is much easier to compare $6.3 \cdot 10^{13}$ and $5.4 \cdot 10^{14}$ than $63000000000000$ and $540000000000000$.

The difference between the modes is the following: In scientific mode, there will be exactly one non-zero digit in front of the decimal point, i.e. a number is represented as $m \cdot 10^e$ with $1 \leq m < 10$ and $e \in \mathbb{Z}$. In engineering mode, there are one to three digits in front of the decimal point and the exponent is divisible by $3$, i.e. $1 \leq m < 1000$ and $3 \mid e$.