Question: I realize this is a somewhat vague question so I'll do my best. If I have a number like `n = 0.783325849821429`, is there a way to display even more decimal places? This was produced with format long. The problem is that I'm doing error estimate calculations with sine and there comes a point where the estimation is so close to the actual value of sine that MATLAB calculates the error as 0, even though it's not possible that the estimation is completely accurate. There's always error, it's just too small for MATLAB to recognize. Is there a way to make MATLAB consider more decimal places?

Answer: 
You can always ask for more digits using [formatted strings](http://www.mathworks.com/help/matlab/matlab_prog/formatting-strings.html)

```
 fprintf(1, 'n = %.20f\n', n ); % print with 20 digits after the decimal point

```

**However** there is a limit to the precision of stored numbers in floating point.  

You can test the machine precision using [`eps`](http://www.mathworks.com/help/matlab/ref/eps.html)

```
eps( n )

```

If your estimate error is smaller than `eps` than your estimate is within machine precision and cannot be measured.
if you use vpa function to increase precision then it will have your variable as syms and after that if u want to use this variable for other matlab internal functions then it will not work hence find some other way.

e.g.

```
a=vpa(a,5) 
a =

[ 1.25, 2.0276, 3.2108, 3.3695, 2.0589, 1.0]

polyval(a,3)

??? Undefined function or method 'isfinite' for input arguments of type
'sym'.

Error in ==> polyval at 54
if isscalar(x) && (nargin < 3) && nc>0 && isfinite(x) &&
all(isfinite(p(:)))

```