Question 966405
Pick a denominator greater than 10, say {{{11}}}.
{{{-11/11=-1}}}
{{{11/11=1}}}
So any number between {{{-11}}} and {{{11}}} in the numerator will give a rational number between {{{-1}}} and {{{1}}}.
{{{-10/11}}}
{{{-9/11}}}
{{{-8/11}}}
{{{-7/11}}}
{{{-6/11}}}
{{{-5/11}}}
{{{-4/11}}}
{{{-3/11}}}
{{{-2/11}}}
{{{-1/11}}}
{{{0/11=0}}}
{{{1/11}}}
There's twelve. 
You could also choose positive numerators,
{{{2/11}}}
{{{3/11}}}
etc.