3
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Consider:

f[x_] := (1 + x)^(1/x);
Manipulate[
 Plot[f[x], {x, -eps, eps}],
 {{eps, 0.00001}, {1, .1, .01, .001, .0001, .00001, .000001},
  ControlType -> SetterBar}]

Which gives this image.

enter image description here

How can I double the number of digits used in the labels for the tick marks on the vertical axis? And how can I replace the scientific notation in the last setter bar choice to pure decimal (i.e..000001)?

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3
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As to your first question

f[x_] := (1 + x)^(1/x)

 eps = 0.00001;

{v, b} = {f@-eps, f@eps};

r = Range[b, v, (v - b)/5.];

Plot[f[x], {x, -eps, eps},
 Ticks -> {Automatic, Transpose[{r, NumberForm[#, {12, 10}] & /@ r}]}]

enter image description here

2nd question

SetterBar[1, MapThread[Rule, {#, AccountingForm /@ #} &
  [{1, .1, .01, .001, .0001, .00001, .000001}]]]

enter image description here

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