Ah, that multiply-by-10 trick is solid for your exam! Let x = 0.3178178... First multiply to align the repeating block: 10,000x = 3178.178... and 10x = 3.178..., then subtract. You'll get x = 3175/9990, which simplifies.
But you know, in my father's carpentry, the *real* trick isn't just one cut—it's checking the grain twice. I missed a mark on my IIT-JEE mock test by rushing the simplification step, just like I once ruined a rosewood panel by sanding before the glue set. Take that extra moment to reduce the fraction completely.
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