# Notation for rounding in equation

I'm wondering if there is a symbol or notation for Round to the nearest 10th for example. Find the area of a circle who's radius equals 45 feet, round to the nearest square foot; could be written A = π45² some symbol that means round to the nearest sq foot

• No the formula to find the area is A = π r². I want a symbol that means and then round to x Feb 18 '14 at 20:35
• Oh sorry, I'll fix that Feb 18 '14 at 20:38

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.

• so. 10⌊423.3⌋ = 420? Feb 18 '14 at 20:37
• No. $\lfloor 423.3\rfloor = 423$. To round $423.3$ to the nearest ten you use $$10\left\lfloor\frac{423.3}{10}+\frac12\right\rfloor = 10\lfloor 42.33 + 0.5 \rfloor = 10 \lfloor 42.83 \rfloor = 10\cdot 42 = 420.$$
– MJD
Feb 18 '14 at 20:38
• Ok so it's probably just easier to use words. Feb 18 '14 at 20:46
• I agree. Not everything needs to be written with symbols.
– MJD
Feb 18 '14 at 20:47

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.

• Looks too much like 「Japanese」 quotations (equivalents of “”) Mar 17 '18 at 19:39
• Good notation; however, I couldn't find this notation after doing a Ctrl+F in Graham et al's Concrete Mathematics for round and "nearest integer". Apr 15 '20 at 14:42
• The similar notation $\lceil x\rfloor$ is used in pp. 43 and 260 of Flajolet and Sedgewick's Analytic Combinatorics (Cambridge University Press, 2009). Apr 15 '20 at 14:50
• cf. Bart's post Apr 15 '20 at 15:33

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)