(Though perhaps as is suggested with languages, it's better to start applying the new system directly, instead of performing a conversion step first.)
I find that meters are better for thinking about walking measures, why does our system even have a yard? Think in units, metric is good. I learned this in American Public School. I was very lucky.
The exact conversion is 1.609344, so to two places it is 1.61. That's only slightly harder than 1.6. Think of it is 1 + 1/2 + 1/10 + 1/100. So for my prior example, 34 x 1.61 = 34 + 17 + 3.4 + 0.34 = 54.74.
The operations needs, taking 1/2, 1/10, and 1/100 of the original value are generally easy in your head. The hardest thing is just keeping track of the running sum as you do that.
If you want to go one step farther, you could add a -1/1000 term to bring it to 1.609 but that is probably overkill in most circumstances. Even 1.61 is probably overkill.
I got a shocked reaction "you look much smaller!" from someone when I just reported my weight in pounds as weight in 斤. I guess the lesson is it's not "close enough" when people are already sensitive to a particular scale.
*except for when it's not, of course :-)
Loaves of bread in Japan are still sold using 斤 (kin). A standard loaf is one "bread kin" which is defined as 340g or more.