MATLAB Central Newsreader - decimal precision

decimal precision

Young Ryu — Tue, 13 May 2008 18:31:08 -0400

Hi-

I'd like to round at 4th decimal point. For example,

1.41536664
=> 1.415

how can I round at specific precision? There is no syntax
in "round" function.

Thanks!

Re: decimal precision

jay vaughan — Tue, 13 May 2008 18:43:03 -0400

Re: decimal precision

roberson@ibd.nrc-cnrc.gc.ca (Walter Roberson) — Tue, 13 May 2008 18:57:24 -0400

In article <g0cmpc$gjg$1@fred.mathworks.com>,
Young Ryu <ryuyr77@gmail.com> wrote:

>I'd like to round at 4th decimal point. For example,

>1.41536664
>=> 1.415

>how can I round at specific precision?

It is not (generally) possible to round fractions at a decimal precision,
The exceptions have to do with rounding to integers divided by exact powers
of 2, such as 1/2, 1/4, 3/4, and so on.

There is no exact representation in binary floating point for 0.1 (1/10),
just as there is no exact representation in base 10 decimal expression
for 1/3. If your number does not happen to round to one of those
power-of-2 fractions I mentioned before, then there will always be
something left over -- it might be 15 decimal places further down, but
it will be there.

You -can-, though, convert numbers to character strings that
have specific numbers of decimal places, for "presentation purposes"
as the other poster mentioned.
--
  "He wove a great web of knowledge, linking everything together,
  and sat modestly at a switchboard at the center, eager to help."
                                              -- Walter Kerr

Re: decimal precision

Roger Stafford — Tue, 13 May 2008 19:22:03 -0400

"Young Ryu" <ryuyr77@gmail.com> wrote in message <g0cmpc$gjg
$1@fred.mathworks.com>...
> Hi-
>
> I'd like to round at 4th decimal point. For example,
>
> 1.41536664
> => 1.415
>
> how can I round at specific precision? There is no syntax
> in "round" function.
>
> Thanks!
----------
  You haven't made it clear whether it is only the display of a number or the
actual number matlab is using in its computations that is to be altered. There
is an important difference between the two, though new users often do not
distinguish between the two concepts.

  If you want to display a number to four significant figures, do this:

fprintf('The number n equals: %12.4e\n',n)

  On the other hand, if you want to change the number actually stored in
matlab in this manner, do this:

m = 4; % Number of significant decimals
k = fix(log10(abs(n)))-m+1;
n2 = round(10^k*n)/10^k;
fprintf('The altered number is: %30.20e\n',n2)
  = 1.41500000000000003600e+00

  You will note that if you display the altered number to a sufficient accuracy,
it is unlikely to be exactly the fraction you requested. That is because
matlab's 'double' format is unable to exactly represent most decimal
fractions.

Roger Stafford

Re: decimal precision

Roger Stafford — Wed, 14 May 2008 00:24:01 -0400

"Roger Stafford" <ellieandrogerxyzzy@mindspring.com.invalid> wrote in
message <g0cpor$h3v$1@fred.mathworks.com>...
> You haven't made it clear whether it is only the display of a number or the
> actual number matlab is using in its computations that is to be altered.
There
> is an important difference between the two, though new users often do not
> distinguish between the two concepts.
>
> If you want to display a number to four significant figures, do this:
>
> fprintf('The number n equals: %12.4e\n',n)
>
> On the other hand, if you want to change the number actually stored in
> matlab in this manner, do this:
>
> m = 4; % Number of significant decimals
> k = fix(log10(abs(n)))-m+1;
> n2 = round(10^k*n)/10^k;
> fprintf('The altered number is: %30.20e\n',n2)
> = 1.41500000000000003600e+00
>
> You will note that if you display the altered number to a sufficient
accuracy,
> it is unlikely to be exactly the fraction you requested. That is because
> matlab's 'double' format is unable to exactly represent most decimal
> fractions.
>
> Roger Stafford
------------
  I was hasty in my earlier response and made three errors. I should have
said:

1) To display n to four significant decimals, do:

fprintf('The number n equals: %10.3e\n',n)

2) To actually alter the number n to the nearest four place decimal, do:

m = 4; % Number of significant decimals
k = floor(log10(abs(n)))-m+1;
n2 = round(n/10^k)*10^k;

  a) The most serious error I made was multiplying n by 10^k instead of
dividing by it. That really makes a mess of it!

  b) However, using 'fix' instead of 'floor' is also an error, giving one too few
significant decimal places for numbers less than 1.

  c) In 1) with %12.4e it would result in 5, not 4, significant decimals being
displayed.

  Sorry about all that! Perhaps I stayed up too late last night.

Roger Stafford