Two, now three, ways:  I think I'd recommend the first -- strike that -- maybe the third one at the end, but perhaps you have a reason for using SetPrecision, in which case, use the second.

This first one works as is.  One caveat: if the label is used as an input field, the number k will be set to a machine-precision number.

Manipulate[
 Plot[Cos[k x], {x, 0, 2 Pi}],
 {{k, 1}, 0.`22, 4.`22, 0.1`22, Appearance -&gt; "Labeled"}]


The second way is to make your own label.  Here editing the label still maintains the desired precision.

Manipulate[
 Plot[Cos[k x], {x, 0, 2 Pi}],
 {{k, 1}, SetPrecision[0., 22], SetPrecision[4.0, 22], SetPrecision[0.100, 22], 
  Row[{Manipulator[##], "  ", 
     InputField[Dynamic[Round[k, 0.1], (k = SetPrecision[#, 22]) &amp;], 
      Appearance -&gt; "Frameless", BaseStyle -&gt; "Label"]}] &amp;}
 ]


Here is a variation with a non-editable label:

Manipulate[
 Plot[Cos[k x], {x, 0, 2 Pi}],
 {{k, 1}, SetPrecision[0., 22], SetPrecision[4.0, 22], SetPrecision[0.100, 22],
  Row[{Manipulator[##], "  ", Dynamic@Round[k, 0.1]}] &amp;}]


Both look the same.





There is a difference between setting the precision with SetPrecision and with a backtick:

x = SetPrecision[0.1, 22]
(* 0.1000000000000000055511 *)

y = 0.1`22
(* 0.1000000000000000000000 *)

Precision /@ {x, y}
(* {22., 22.} *)

x - y
(* 5.5511*10^-18 *)




Alternatively, you can use a dummy variable and convert it to the desired precision:

Manipulate[
 k = N[Round[k0, 1/10], 22];
 Plot[Cos[k x], {x, 0, 2 Pi}, PlotLabel -&gt; k],
 {{k0, 1, "k"}, 0, 4, 0.1, Appearance -&gt; "Labeled"},
 {k, None},
 TrackedSymbols :&gt; {k0}]


(I included a plot label to verify that k has the proper precision.)

How to set precision and format labeled Slider in Manipulate?
Out of necessity, I had to put an 1.26" (32mm) rear tyre on my bike where the front tyre is only 1.1" (28mm) wide (and the bike came with 1.1" tyres when I bought it). Are there any advantages or disadvantages of this, shall I try to get an 1.1" tyre for the rear wheel ASAP or is it safe this way?
