Question 1006486
If the diameter decreases by {{{"5%"}}} ,
it becomes {{{"100%"-"5%"="95%"=95/100=0.95}}} of the original diameter.
As a consequence, the cross-section surface area,
{{{area=pi*diameter^2/4}}} ,
becomes
{{{new_area=pi*new_diameter^2/4=pi*(0.95*diameter)^2/4=pi*0.95^2*diameter^2/4=0.95^2*(pi*diameter^2/4)=0.95^2*area=0.9025*area}}} .
It becomes {{{0.9025=90.25/100="90.25%"}}} of the original cross-section surface area.
As the wire can be considered a cylinder,
with a base the same size/shape as the circular cross-section,
and the length of the wire for a height,
the original wire's volume is
{{{volume=area*length}}} .
The new wire's volume is
{{{new_volume=new_area*new_length=0.9025*area*new_length}}} .
Since that volume has to be the same,
{{{0.9025*area*new_length=area*length}}}-->{{{0.9025*new_length=length}}}-->{{{new_length=length/0.9025}}}
The relative change in length is
{{{(new_length-length)/length=(length/0.9025-length)/length=length/0.9025/length-length)/length=1/0.9025-1=about0.108033}}}{{{(rounded)=10.8033/100}}}{{{(rounded)="10.8033%"}}}{{{(rounded)}}} .
We cannot give an exact decimal value,
we have to give a rounded, approximate result,
as {{{"10.8%"}}} , or {{{"11%"}}} , for example,
because {{{1/0.9025}}} and {{{1/0.9025-1}}} written as decimals would have an infinite number of digits.
Since we start with two significant figure in {{{"95%"}}},
reporting the result as {{{"10.8%"}}} (very similar precision),
or {{{"11%"}}} (same number of significant digits) makes sense.
 
NOTE:
If all that talk about precision and significant figures, doesn't make sense to you, pretend that I did not write that.