There are other reasons, though, that a rational approximation can be useful. If you're doing mental arithmetic, for example, multiplying by a fraction can be e

There are other reasons, though, that a rational approximation can be useful. If you're doing mental arithmetic, for example, multiplying by a fraction can be easier than multiplying by a decimal, but this depends on the specific numerator and denominator. In this way, 22/7 fails horribly, because multiplying by 22 and dividing by 7 are not particularly easy operations. For example, 100/32 is a less accurate representation than 22/7, but it is far easier to multiply, since you can do so with only two mental registers. In fact it also takes fewer registers to multiply than 3.1 (which is also less accurate than 100/32). However, it does require more mental operations than 3.1; 100/32 takes five halvings and a decimal shift, while 3.1 requires multiplication-by-3, a decimal shift, and an addition. What would be really cool would be an analysis similar to the one in the article that used a model of mental computation to find the best tradeoff for working numbers in your head. That said, for mental calculations you're probably better off just pretending that pi = 3, unless you're just trying to impress someone.