What is the correct symbol for "equal-rounded"? What is the correct symbol for saying "equals, but is rounded"? For example:
$$\frac{1}{17}=0.0588$$
Is not essentially correct, since it's rounded. What other equal-like symbol should I use?
 A: I use $=$ for equaility, $\approx$ for approximately equal to, and $\doteq$ for correctly rounded to. So
$$\frac{1}{17} = 0.058823529\ldots \qquad \text{and} \qquad \frac{1}{17} \approx 0.06,$$
while
\begin{align*}
\frac{1}{17} &\doteq 0.1 \quad (\text{1 decimal place appears so result is correctly rounded to 1 decimal place})\\
\frac{1}{17} &\doteq 0.06 \quad (\text{2 decimal places appears so result is correctly rounded to 2 decimal places})\\
\frac{1}{17} &\doteq 0.059 \quad (\text{3 decimal places appears so result is correctly rounded to 3 decimal places})\\
\frac{1}{17} &\doteq 0.0588 \quad (\text{4 decimal places appears so result is correctly rounded to 4 decimal places})\\
\frac{1}{17} &\doteq 0.05882 \,\, (\text{5 decimal places appears so result is correctly rounded to 5 decimal places})\\
\end{align*} 
and so on.
A: Answer from comments:


*

*Usually one writes $\dfrac 1 {17} \approx 0.0588.$

*One can write $\dfrac 1 {17} = 0.0588\ldots,$ meaning there are further digits after the $8.$  I would use the notation $\text{“ } =0.0588\ldots \text{ ''}$ only if that last explicit digit is $8$ and not if it's rounded upward to $8,$ whereas I would use $\text{“ } \approx 0.0588 \text{ ''}$ if it's rounded either upward or downward. (But in this case this is not an issue since $1/17 = 0.0588235\ldots$)
A: ", which rounds to".  For example "... yielding $\frac{1}{17}$, which rounds to 0.0588."  This follows the old rule: "say what you mean and mean what you say".

A parable
Years ago someone gave me a fancy clock that shows the time of day as words.  However, some time last week, it stopped and only shows "noon" now.  There's an old adage "a stopped clock is right twice a day" (assuming a 12 hour clock).  This clock is clearly correct once per day.  What fraction of the day is it approximately correct?  That is, for how many seconds of the day is the time "$\approx$ noon"?
Unless and until you specify what you mean by "$\approx$", the question is meaningless.  For instance, with what precision is the indicated time, "noon"?  Does the clock only indicate hours, also minutes, also seconds, all the way down to ... what? nanoseconds?  Does it generate an additional 100 random digits, claiming absurd precision (necessarily without any promise of accuracy)?  Then, when you say "$\approx$", how accurate must that value of unknown precision be? Within $\pm \frac{1}{2}$ day? $\pm \frac{1}{2}$ hour? $\pm \frac{1}{2}$ minute? $\pm \frac{1}{2}$ second? $\pm \frac{1}{2}$ nanosecond? $\pm \frac{1}{2} \times 10^{-100}$ nanosecond?  What do you do with the endpoints of these accuracy intervals; are they $\approx$ or not?  Do you include both endpoints, one (which one?), neither?  What if you know the clock was always set an hour fast?  Do you account for that systematic error in $\approx$ or not?
An approximation scheme has to specify all of these things.  The function of mathematical notation is precision of expression.  "$\approx$" inadequately specifies, so cannot be precise.  For instance is "$100 \approx 0$" true or false?  (Are we rounding to nearest millions?  Where is that in the notation?)

One might claim that the same applies to my suggested phrase, "which rounds to".  There are dozens of standard rounding techniques.  If we restrict to computation, IEEE 754 specifies five rounding techniques.  Conveniently, each of these techniques resolves all of the questions asked above.  Also conveniently, the standard rounding technique is round to nearest increment with ties rounding up.  If you mean some other kind of rounding, you have to say so.  If, as I have suggests, you write out what you are doing to transform your exact quantity into your reported result, you have an easy place to say that you mean some other kind of rounding.
