Smoke Alarm

Joyce had badgered me for some time to install a smoke alarm upstairs and on our last trip to Lowes she just threw one into our cart. It was my task to assemble and install it.
The instructions called for drilling a pair of 3/16 holes in the sheetrock wall. I looked in my drill holder and saw no 3/16 drill. I didn’t want to drill a hole too big, so I looked at what I had and then tried to figure out which one to use to get a drill just slightly smaller than 3/16. I had a 1/16, 5/64, 3/32, 7/64, 1/8, 9/64, 5/32, 11/64, 7/32, 1/4, and 5/16. My thinking was not too good that day as I could have mechanically figured out what drill to use easily. All I could think of was how to convert 3/16 to one of the numbers above. My working with fractions was more than a little out of habit, as yours may be, so which drill I use?
Take your time to figure it out; I’ll wait for your answer. I know some will find it easy to figure while others will find it mind boggling.