That I leave up to the context. In certain areas, or goals, precision to dozens of decimal places is not only necessary, but it is also a thing of beauty. One needs to look no further than to the disastrous first images from the Hubble telescope to see that. In others, such as figuring out if your American friends are getting sunburnt or frostbitten... conserving time ekes out precedence.
Precision in itself risks becoming fanatical, self absorbed, pointless. This is not to say that sloppiness should be revered, but rather that mechanical progress should be tempered with a respect for human craftmanship. I am all for being specific in one's language, for vague references are the cover of foolsābut I also see limits for rationality being breached now and then.