After reviewing your code on jsFiddle (http://jsfiddle.net/qGJhe/), I decided to test adding a background color to the container to investigate the reported extra gap issue. Surprisingly, no extra gap was visible.
Although your specified 960px width was not being honored due to the responsive nature of the layout, it became apparent that the codes you copied over might have some discrepancies from your actual page.
To counter this and enforce the fixed 960px width, I disabled the responsive code temporarily and observed the additional 10px gap as described. http://jsfiddle.net/shodaburp/qGJhe/3/
This led me to the realization that there were inaccuracies in your calculation for both the gutter size and the element's width.
It appears that an element width of 240px leaves no room for the gutter at all. http://jsfiddle.net/shodaburp/qGJhe/4/
gutterSize = (containerWidth - (elementWidth * numberOfElement) / numberOfGutters)
gutterSize = (960 - (240 * 4) ) / 3) = 0
totalWidth = (elementWidth * numberOfElement) + (gutterSize * numberOfGutters)
totalWidth = (240 * 4) + (3 * 0) = 960
extraGap = containerWidth - totalWidth
extraGap = 960 - 960 = 0
A slight adjustment with an element width of 230px along with a gutter size of 13 reveals a 1px extra gap. http://jsfiddle.net/shodaburp/qGJhe/5/
gutterSize = (containerWidth - (elementWidth * numberOfElement) / numberOfGutters)
gutterSize = (960 - (230 * 4) ) / 3) = 13.33 = 13 (rounded)
totalWidth = (elementWidth * numberOfElement) + (gutterSize * numberOfGutters)
totalWidth = (230 * 4) + (3 * 13) = 959
extraGap = containerWidth - totalWidth
extraGap = 960 - 959 = 1
To ensure a perfect fit for 4 elements within the 960px space, consider adjusting the element width to 225px alongside a 20px gutter size.
An element width of 225px combined with a gutter size of 20px will achieve optimal spacing! http://jsfiddle.net/shodaburp/qGJhe/6/
gutterSize = (containerWidth - (elementWidth * numberOfElement) / numberOfGutters)
gutterSize = (960 - (225 * 4) ) / 3) = 20
totalWidth = (elementWidth * numberOfElement) + (gutterSize * numberOfGutters)
totalWidth = (225 * 4) + (3 * 20) = 960
extraGap = containerWidth - totalWidth
extraGap = 960 - 960 = 0