? ratprint;

Calculate

ratprint:off;

Calculate

? ratprint;

Calculate

ratprint:off;

Calculate

### ratprint

Run Example
```(%i1)rat(0.1234);

rat: replaced 0.1234 by 617/5000 = 0.1234
617
(%o1)/R/                             ----
5000
(%i2) rat(0.12345);

rat: replaced 0.12345 by 2469/20000 = 0.12345
2469
(%o2)/R/                             -----
20000
(%i3) rat(0.12345);

rat: replaced 0.12345 by 2469/20000 = 0.12345
2469
(%o3)/R/                             -----
20000
(%i4) mod(12345, 1000)/100000, numer;
(%o4)                               0.00345
(%i5) lastdigits(fnum, lastn):=block([m:10*fnum, ans, n:lastn], /* it doesn't help when lastn is bigger than the total digits in fnum it returns the whole digits in fnum anyway without erroring! and fnum=%pi stuff works only upto 8 digits cause num(rat(fnum)) has somuch only! */ratprint:false, k:rat(fnum), ans:mod(m, (10^-n))/(mod(m, 10)*denom(k)), return(float(ans)));
(%o5) lastdigits(fnum, lastn) := block([m : 10 fnum, ans, n : lastn],
- n
mod(m, 10   )
ratprint : false, k : rat(fnum), ans : -------------------, return(float(ans)))
mod(m, 10) denom(k)
(%i6) lastdigits(0.12345, 3);
(%o6)                        2.0251113811259619E-8
(%i7) ```
Run Example
```load(basic);
define: warning: redefining the built-in function prog1
define: warning: redefining the built-in function symbolcheck
define: warning: redefining the built-in function push
define: warning: redefining the built-in function pop
define: warning: redefining the built-in function tr_ev
(%o1)           /usr/share/maxima/5.21.1/share/macro/basic.mac
(%o2)      /usr/share/maxima/5.21.1/share/simplification/functs.mac
(%i3)  ratprint:false;
(%o3)                                false
(%i4) setify(makelist(1/k, k, 1, ceiling(rat(0.1))));
(%o4)                                 {1}
(%i5) ```
Run Example
```kill(lastdigits,pidigits, a, b);
(%o1)                                done
(%i2) ratprint:false;
(%o2)                                false
(%i3) pidigits(prec):=block([fpprec:prec+1], ratprint:false, bftorat:false, ratepsilon:2.0e-16, float2bf:false, ans:float((%pi-mod(%pi, 10^(-prec)))), return(ans));
(%o3) pidigits(prec) := block([fpprec : prec + 1], ratprint : false,
bftorat : false, ratepsilon : 2.0E-16, float2bf : false,
- prec
ans : float(%pi - mod(%pi, 10      )), return(ans))
(%i4) lastdigits(fnum, lastn):=block([m:rat(fnum), n:lastn, ans], /* it doesn't help when lastn is bigger than the total digits in fnum it returns the whole digits in fnum anyway without erroring! and fnum=%pi stuff works only upto 8 digits cause num(rat(fnum)) has somuch only! */ratprint:false, ratio(num):=block([k, a], ratprint:false, for k:1 thru fpprec do (a:10^k/ratdenom(num), if(integerp(a)) then return(a))), ratepsilon:2.0e-16, bftorat:false,  ans:mod(ratio(fnum)*num(m), (10^n))/(ratio(fnum)*denom(m)), return(float(ans)));
(%o4) lastdigits(fnum, lastn) := block([m : rat(fnum), n : lastn, ans],
ratprint : false, ratio(num) := block([k, a], ratprint : false,
k
10
for k thru fpprec do (a : -------------, if integerp(a) then return(a))),
ratdenom(num)
n
mod(ratio(fnum) num(m), 10 )
ratepsilon : 2.0E-16, bftorat : false, ans : ----------------------------,
ratio(fnum) denom(m)
return(float(ans)))
(%i5) lastdigits(4.1459, 5);
(%o5)                          4.14590001103631
(%i6) lastdigits(3.1459, 3);
(%o6)                               0.0459
(%i7) b:pidigits(5);
(%o7)                               3.14159
(%i8) lastdigits(3.14159, 3);
(%o8)                               0.00159
(%i9) lastdigits(pidigits(5), 3);
(%o9)                               0.00159
(%i10) pidigits(6);
(%o10)                             3.141592
(%i11) lastdigits(pidigits(6), 3);
(%o11)                       5.9199999999999997E-4
(%i12) lastdigits(4.14592, 3);
(%o12)                              0.00592
(%i13) lastdigits(b, 3);
(%o13)                              0.00159
(%i14) a:[0, float(%pi)];
(%o14)                      [0, 3.141592653589793]
(%i15) a;
(%o15)                      [0, 3.141592653589793]
(%i16) delete(pidigits(16), a);
(%o16)                                [0]
(%i17) delete(pidigits(fpprec), a);
(%o17)                                [0]
(%i18) delete(pidigits(fpprec), [0, float(%pi)]);
(%o18)                                [0]
(%i19) intervals(items, [granul]):=block([ start:first(items), stop:last(items), ans:[], granul:(if not(emptyp(granul)) then first(granul) else 1) ], ratprint:false, if (emptyp(items)) then [] elseif(listp(items)) then    if(emptyp(rest(items))) then []     else     while(float(rat(start))<
float(rat(stop))) do    (ans:delete([],             delete([float(rat(stop)), float(rat(stop+granul))],             if(float(rat(start+granul))>
float(rat(stop)))            then return() else            append(ans, [cons(float(rat(start)),  [float(rat(start+granul))])]))),      start:float(rat(start+granul))),     return(ans));
(%o19) intervals(items, [granul]) := block([start : first(items),
stop : last(items), ans : [], granul :
if not emptyp(granul) then first(granul) else 1], ratprint : false,
if emptyp(items) then [] elseif listp(items)
then (if emptyp(rest(items)) then [] else (while float(rat(start)) <
float(rat(stop)) do (ans : delete([], delete([float(rat(stop)),
float(rat(stop + granul))], if float(rat(start + granul)) > float(rat(stop))
then return() else append(ans, [cons(float(rat(start)),
[float(rat(start + granul))])]))), start : float(rat(start + granul))))),
return(ans))
(%i20) intervals([0, 2*%pi], %pi);
(%o20) [[0.0, 3.141592653589793], [3.141592653589793, 6.283185307179585]]
(%i21) delete(pidigits(fpprec), intervals([0, 2*%pi], %pi));
(%o21) [[0.0, 3.141592653589793], [3.141592653589793, 6.283185307179585]]
(%i22) ```

### Related Help

Help for Ratprint