There are frequent questions on the MATLAB newsgroup about rounding results to a certain number of decimal places. MATLAB itself doesn't provide this functionality explicitly, though it is easy to accomplish.
Contents
Sidetrack : A Little MathWorks History
MathWorks' first Massachusetts office phone number was 653-1415 (ignoring country and area codes). The astute reader will
notice that the last 5 digits are an approximation for 
(or, in MATLAB, pi). A local resident called one day to say that she kept getting calls for MathWorks and she wasn't sure why. But it was quite
inconvenient for her because she spent lots of time on the second floor of her home, and the phone was on the first floor.
The excess round-trips were taxing her! To understand what was happening, you should know that in some of the early MathWorks
materials, the phone number was listed as 
.
Example
format long
x = 1.23456789x = 1.234567890000000
Use round. Here we get no decimals at all.
round(x)
ans =
1
There are many ways to get the number of decimals you want. Here's one way to round to 3 decimals.
round(x*1000)/1000
ans = 1.235000000000000
Here's another way.
sprintf('%0.3f',x)ans = 1.235
And another. In this case, using the "easy" way to specify the format, you need to know how many integral digits there are as well.
str2num(num2str(x,4))
ans = 1.235000000000000
Tools for Rounding Solutions
There are a lot of tools for helping you round numbers. The functions I list here for MATLAB form the basis of many, if not all, of the specific solutions.
MATLAB
Mapping Toolbox
File Exchange Rounding Tools
% N= num2str(X,SF); % N= str2num(N);
Question for You
When you round values, do you want this for display only, or wanted for calculations? Some applications I can think of might include processing data that has a smaller number of bits of precision to start with. What applications do you need rounding for in your calculations? Post here with your thoughts.
Get
the MATLAB code
Published with MATLAB® 7.8
Dear Loren,
I have used the first option you mention several times, and it’s been always for the post-processing part and never for the calculations.
Greets
I’ve used things like ceil(x/1000)*1000 to calculate axis limits for pretty graphs. I think it’s nice when there’s a label at the top end of the axis, especially with logarithmic scaling.
Counting derangements:
For display I allways use the *printf() version.
For calculations, the first method proposed is the only one I find reasonable, even if it doesn’t exactly give the most readable code.
Sometimes I use a method not presented here, and that is the typecast method. Of course, it only makes sense when you want to round to the classical number formats, but you are absolutely sure you get what you want.
[65 pi], that’s a fun round-about story. Her phone number was 653-1416, correctly rounded, wasn’t it? Her round trips were rounded up.
If you need a few more digits (4,493 of them) just look at my T-shirt :-)
http://www.thinkgeek.com/tshirts-apparel/unisex/sciencemath/6e7e/
But the best round is another one. Cheers!
>> floor(22*(15/22)) ans = 14 >> floor(49*(1/49)) ans = 0Ben-
Obviously you still need to be aware of numerical round-off in the calculations done before rounding in the first place. And using floor instead of round may not be what you want to do.
–Loren
Loren,
I use rounding for calculations and comparisions with specification limits. For example if the lower spec limit is 1.8 and the calculated value is 1.78254343 I want this value to pass because it rounds to 1.8 which is not less than the specification limit. This may not be ‘correct’ but it’s the way we’ve done our spec checking since time immemorial (in computer terms anyway).
Craig
Craig-
I’m glad rounding works for you. Are you rounding to tenths for your work? Is your target value always in in tenths? Another possibility is to check if the calculated value is within a certain distance from the spec (e.g., abs(spec-calc) < SomeTolerance).
–Loren
The illustrates why MatLab needs a smarter round function, much like even lowly Excel has, where the user can specify the number of digits to which you want to round to.
OysterEngineer-
I recommend you use the support link on the right to enter your suggestion for round. Suggestions directly from customers tend to carry more weight. Thanks.
–Loren