Reading a Digital Timer

Many digital timers show the elapsed time to one hundredth of a second. What is the minimum uncertainty in the value? What value should be reported?

Answer

For a digital timer that displays the elapsed time to one-hundredth of a second, the minimum uncertainty in the interval depends on the software and/or hardware method used to display the last digit. Suppose that the hundredths digit fraction from 0.00 through 0.49 is displayed as zero hundredths and from 0.50 through 0.99 is displayed as one hundredth. Likewise, 1.00 through 1.49 is displayed as one hundredth, and 1.50 through 1.99 as two hundredths. Seeing a 1 in the hundredths place then corresponds to the range from 0.50 through 1.49, so the minimum uncertainty in the elapsed time value is ± 0.50, or one-half of one-hundredth of a second. The reported elapsed time should be given as, say, 3.45 seconds ± 0.005 second, which is an awkward notation, because the display goes only to hundredths of a second, yet the uncertainty is smaller. Therefore, by agreement, the elapsed time is given as 3.45 seconds ± 0.01 second so that the number of decimal places is the same for the value and the uncertainty that is, there is an uncertainty of plus or minus one digit in the smallest time interval position of the display.

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