Notation for rounding in equation
I'm wondering if there is a symbol or notation for Round to the nearest 10th
For example, the area of a circle with a radius of 45 feet, rounded to the nearest square foot, could be written as, A = π45²sym
Where sym is some symbol that means round to the nearest sq foot
3 Answers
$\begingroup$There isn't a simple notation for that. In the past fifty years or so the notation $\lfloor x\rfloor$ has become common to mean the greatest integer that is not more than $x$. For example $\lfloor 8.9\rfloor = \lfloor 8.5 \rfloor = \lfloor 8.2 \rfloor = \lfloor 8 \rfloor = 8$.
The result of rounding $x$ to the nearest integer is $$\left\lfloor x+\frac12\right\rfloor.$$
If you want to round to the nearest 10, you can then do $$10\left\lfloor \frac x{10}+\frac12\right\rfloor$$ which rounds $\frac{x}{10}$ to the nearest integer, then multiplies by 10 again. Replacing the 10 with something else such as 17 will round to the nearest multiple of 17 or whatever; in particular $$\frac1{10}\left\lfloor 10x+\frac12\right\rfloor$$ will round to the nearest tenth.
$\endgroup$ 4 $\begingroup$I have come across the following notation: $\lfloor 12.3 \rceil=12$ or $\lfloor 12.7 \rceil=13$.
I think that I have seen it in the "Concrete Mathematics" book by Graham, Knuth and Patashnik.Anyway that notation combines neatly the ceiling and floor function. However, I wouldn't say that it has become a standard notation yet.
$\endgroup$ 5 $\begingroup$I like the combined floor/ceiling symbol for nearest integer, although Wolfram calls it "cumbersome" and "not recommended". When I was at school, if you wanted to show an answer was rounded to the nearest 10th, you'd put "(to 1dp)" after it, where "dp" stands for "decimal place". An alternative approach to rounding was "(to 3 sf)" where "sf" means "significant figures". Eg 12345.67 = 12345.6 (to 1 dp) or 12300 (to 3 sf) 12.34567 = 12.3 (to 1 dp) or 12.3 (to 3 sf)
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