Half the Decimal Trick

If something happened 1,234 out of 10,000 times, we'd estimate that the true probability of occurence is about 0.1234. Of course, we wouldn't expect the true probability to be exactly 0.1234, and to quantify the uncertainty in this estimate statisticians have long computed confidence intervals. But in this particular case, there's a simple eyeballing trick we can use to get approximate error bars: we round the proportion to half the number of decimal places, (0.12|34 becomes 0.12), and add a plus or minus 1 in the least significant digit, (0.12 +/- 0.01).