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Re: Rounding to a certain number of decimal places

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  Re: Rounding to a certain number of decimal places Bill Rowe <readnews@sbcglobal.net> - 2011-05-28 11:19 +0000

#2760 — Re: Rounding to a certain number of decimal places

On 5/27/11 at 6:14 AM, adeyoung@andrew.cmu.edu (Andrew DeYoung)
wrote:

>I would like to be able to round a number to a certain, specified
>number of decimal places (not number of digits), including zeros.
>Suppose that some function f does this, and takes two arguments, the
>number to be rounded and the number of decimal places to which to
>round:  f[number, numPlaces].  Then, for example, I would like the
>following results, if possible:

>f[0.8168, 3] = 0.817
>f[1.8168, 3] = 1.817
>f[10.8168, 3] = 10.817
>f[100.8168, 3] = 100.817
>f[0.99, 3] = 0.990
>f[0.9, 3] = 0.900
>f[0.00572, 3] = 0.006

>Is there a function f (either built-in or a custom function) that
>can do this?

Except for .99 and .9 the answer is yes. Round will do what you
want. Specifically,

In[1]:= Round[{0.8168, 1.8168, 10.8168, 100.8168, 0.99, 0.9,
   0.00572}, .001]

Out[1]= {0.817,1.817,10.817,100.817,0.99,0.9,0.006}

or if you prefer to specify the number of places past the
decimal point

f[x_, n_] := Round[x, 10^-n]

>Mathmatica's built-in function NumberForm does not
>quite do this because the user specifies the number of digits, not
>the number of decimal places.  Also, NumberForm does not count zeros
>after the decimal point as digits, nor does it add extra zeros as
>needed if they are redundant.

Actually, NumberForm can be used. For example,

In[3]:= NumberForm[.9, {1, 3}]

Out[3]//NumberForm= 0.900

or

In[4]:= NumberForm[10.8168, {5, 3}]

Out[4]//NumberForm= 10.817

In fact for the case of .9 and .99 you have to use something
like NumberForm since Mathematica will not display trailing
zeros for any function that returns a number.

Note, there is a key difference between Round[x,.001] and
NumberForm[x,{n,3}]. Round outputs a value that is different
from the starting value that can be used in subsequent
computation. NumberForm controls the display of the value by
putting a wrapper around the expression being evaluated. The
point is you can do something like

In[5]:= Rationalize@Round[10.8168, .001]

Out[5]= 10817/1000

which demonstrates Round actually changes the value. But you
cannot do something similar with NumberForm.

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