# What's the equivalent to floor(x) and ceil(x) for real numbers?

Are there equivalents to the notation of $\lfloor x \rfloor$ and $\lceil x \rceil$ that don't round to the next integer, but to a specified digit of a real number?

Examples

• $floorReal(2.3656, 1) = 2.3$
• $ceilReal(2.3678, 2) = 2.37$

Do notations for these exist in a mathematical sense? I know such functions exist in programming languages, but what would be the formal mathematical way to write something like this?

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You can use, say, $\frac{1}{100} \lfloor 100 x \rfloor$ and so forth. – Qiaochu Yuan Oct 12 '12 at 21:18
You can always define a function like this if you need it as QiaochuYuan did. Mathematically, it is of interest whether a real number happens to be an integer (and hence it is of interest to determine the nearest integers of a real), but hardly whether multiplication with an arbitrary number like $10^k$ (why not $\pi\sqrt 2$ instead?) makes it an integer. That may be the reason why the extended concept is not widespread in math - it "only" applies to input/output interfaces using limited decimal digits. – Hagen von Eitzen Oct 12 '12 at 21:34