Many times one needs to convert only approximately between metric and inferial* values.
Converting dimensions expressed in mm to inches in your head is easy. You need to divide by 25.4 which is the same as multiplying by 0.03937 which is very close to 0.04 which is 4/100. Simply double the metric dimension twice and move the decimal two places to the left. The error associated with this approach is only 1.6%.
Example: 37 mm -> 74 -> 148 -> 1.48 in (correct value = 1.4567 in}
Converting an inferial fraction expressed as a ratio to mm is also done by dividing by 25.4. Now 25.4 is very close to 256/10 and dividing by this number is the same as multiplying by its inverse 10/256. Since 256 is a power of two and the denominator of any inch fraction is also a power of two, this suggests the following procedure:
Keep doubling numerator and denominator until the denominator is 256. Then the numerator divided by ten is the equivalent in mm with an error of only 0.78%
Example: 13/64 in = 26/128 = 52/256 -> 52/10 -> 5.2 mm (correct value = 5.159375 mm)
* I live in the USA, the only industrial nation on earth that hasn't adopted the metric system. Usonians will tell you that we use the Imperial system but that isn't strictly true. True, we obtained most of our system from Britain but we further botched and confused it into the mess now known as American Customary Units. That's a mouthful to say or write and few will know what you're talking about.
I decided to make up my own designation for a system that has seven different units all called "barrel". My "inferial" is a portmanteau of "inferior/infuriating" and "Imperial".