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Introduction to Marine Engineering

Massachusetts Maritime Academy

Subsection 2.3.4 Decimal Time

When performing navigational calculations, time intervals must be added and subtracted. This is inconvenient and error prone when using the ordinary h:m:s (hours:minutes:seconds) system, so minutes and seconds are expressed as a decimal fraction of an hour instead. For example, six minutes is equivalent to one tenth of an hour. This method is called decimal time.
Table 2.3.5.
Metric time Decimal time
6 minutes 0.1 hours
30 minutes 0.5 hours
45 seconds 0.0125 hours
The following two examples show how to manually convert back-and-forth between metric and decimal time. Most calculators have a built-in function to do this.

Example 2.3.6. Convert to h:m:s to decimal time.

Convert a time interval of 3:24:45 (3 hours, 24 minutes and 45 seconds) to decimal time
Answer.
\begin{equation*} 3:24:45 = \hr{3.4125} \end{equation*}
Solution.
  1. Convert 24 minutes to hours.
    \begin{equation*} \minute{24} = \minute{24} \times \left[ \frac{\hr{1}}{\minute{60}} \right] = \hr{0.4} \end{equation*}
  2. Convert the seconds to hours.
    \begin{equation*} \second{45} = \second{45} \times \left[ \frac{\hr{1}}{\second{3600}} \right] = \hr{0.0125} \end{equation*}
  3. Find the decimal time by adding the minutes and seconds values from steps 1 and 2 to the hours.
    \begin{equation*} 3:24:45 = \hr{3} + \hr{0.4} + \hr{0.0125} = \hr{3.4125} \end{equation*}

Example 2.3.7. Convert decimal time to h:m:s.

Convert a decimal \(\hr{12.947}\) time interval to metric h:m:s time.
Answer.
\begin{equation*} \hr{ 12.947} = \hr{12}:\minute{56}:\second{49.2} \end{equation*}
Solution.
  1. Start with the given value: \(t = \hr{12.947}\)
  2. The whole number portion of this value are the hours.
  3. Subtract the hours, and multiply the remainder by 60. The whole number portion of the result are the minutes.
    \begin{equation*} \hr{0.947} \times \left[\frac{\minute{60}}{\hr{1}}\right] = \minute{56.820} \end{equation*}
  4. Subtract the minutes, and multiply the remainder by 60. The result are the seconds.
    \begin{equation*} \minute{0.820} \times \left[\frac{\second{60}}{\minute{1}}\right] = \second{49.2} \end{equation*}
    If the results are not a whole number, you may round the result to the nearest second if you don’t need fractional second accuracy.
  5. Result: \(t = \hr{12}:\minute{56}:\second{49.2}\)
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