1.6 is the factor everyone talks about (approximation of 1.609), but it has 2 significant figures. To make mental calculations easier/quicker I use its reciprocal, 0.621, which I approximate with 0.6, which has only one significant figure, 6.
Instead of multiplying by 1.6 you would divide by 0.6, which basically amounts to dividing by 6 and then moving the decimal point to someplace plausible.
55 mi / 6 = about 9, so 90 km (actual answer is 88.5)
Going the other way:
80 km * 6 = 480, so 48 mi (actual answer is 49.7)
If you can't remember whether to multiply or divide, just remember multiplying a number by 0.6 makes it smaller, which you would do if going to miles (which are bigger so there are fewer of them). And dividing by 0.6 makes a number bigger, so you must be going to km (which are smaller so there are more of them).