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The correct tool for measuring a small gap with reference to a tolerance is a feeler gauge, which will either slide through the gap or it won't.
Typically used with a straightedge, surface plate or a square for checking the condition of surfaces, feeler gauges can of course be used to measure any small straight gap.
Our feeler gauge sets come from Moore & Wright of Sheffield, they are available in either imperial or metric, marked in thousandths of an inch or mm to -2 decimal places respectively. They are lovely precise tools and have that wonderful oily smell when you open the packet.