Are Your Employee Time Cards Accurate? (The Riddle Of The Missing Dollar)

Time clock software programs are designed to accurately and impartially record employee hours and display those hours clearly and automatically for any given payroll period. There are few things more disconcerting to new time clock software users than to see an occasional employee time card that appears to have a one or two-minute difference between the daily hours worked and the total hours worked for the period.

The answer to this discrepancy is much like the Missing Dollar riddle. Three friends check into a motel for the night and the clerk tells them the bill is $30 for a room, so each pays the clerk $10. A few minutes later, the clerk realizes he's made a mistake and overcharged the trio by $5 so he asks the bellhop to return $5 to the three friends. The bellhop reasons the three friends would have a tough time dividing $5 evenly among themselves, so he decides to only give back $3, while pocketing the other $2. Each of the three friends gets $1 back, thus they each paid $9 for the room which is a total of $27 for the night. Adding this to the $2 the bellhop pocketed amounts to $29 dollars. So where did the other dollar go? The reason this riddle works so well is that it looks obvious a dollar is missing. The reality is that the three men paid $27 ($9 each) for a room the clerk only charged them $25 for. The two extra dollars went into the bellhop's dishonest pocket!

Similarly, when new time clock software users discover 'missing minutes' they are often surprised (and sometimes skeptical) to be told the minutes only appear to be missing. Much like the Missing Dollar riddle, the answer to the missing minutes is how numbers are calculated and displayed in decimal format. Consider an employee who works a 20-minute shift three times a day. How long does the employee work each day? "That's easy!" you say confidently, "20 minutes times 3 equals 60 minutes or one hour per day."

Let's look at a sample time card report with totals displayed as decimals:

08:00 AM to 08:20 AM = .33
12:00 PM to 12:20 PM = .33
05:00 PM to 05:20 PM = .33

Total Hours = 1.0

Since .33 +.33 +.33 =.99, where's the missing time? You see, 20 minutes in decimal format isn't really .33 at all. In reality 20/60 = .3333333 to infinity, but we just use .33 to represent a third of something when in fact it's actually a bit more than .33. So adding .3333333 (to infinity) three times gives us.9999999999 to infinity. In other words, we get a number really close to 1, but not exactly 1. Even if we used really long decimals on our time card reports, we'd still never be able to exactly represent 3 twenty-minute shifts as 60 minutes. So we show 20 minutes simply as .33 hours, which is fine until 3 twenty-minute shifts fail to add up to 1 whole hour!

Make sure your time clock software records employee punch times and performs internal calculations using minutes rather than decimals, so times are always totaled for the exact number of minutes the employee worked. To calculate time cards in decimal format, your time clock software should add up the total minutes worked, divide by 60, and display the total out to 2 decimal places. Since employee time clock software accurately reports every minute an employee works, the missing time is the result of how those mathematical rules you learned in grade school apply to decimal numbers.