Hours and decimal hours: why 7.30 is not 7:30

Two ways to write a duration

In an hours-and-minutes duration, the part after the colon counts minutes. In decimal hours, the part after the point is a fraction of an hour. One hour contains 60 minutes, so the two forms are not interchangeable. A value may look familiar while representing a different amount of work.

Convert in either direction

To convert a duration to decimal hours, multiply its whole hours by 60, add the minutes, then divide that total by 60. To go back, multiply decimal hours by 60, then separate whole hours from the remaining minutes. Use the original value rather than a result that has already been rounded for display.

A common mix-up

7.30 decimal hours means 7 hours plus 0.30 of an hour. That fraction is 18 minutes. So 7.30 hours is 7:18, while 7:30 is 7.50 hours. The difference is twelve minutes, even though the strings share most of their digits.

Keep minutes until the end

Three 20-minute entries total 60 minutes, or exactly 1.00 hour. A two-decimal display of each individual entry is 0.33 hours. Adding those shortened displays gives 0.99 and loses the original exact total. This is a display-precision problem, not an unexplained extra minute in the source record.

Keep the minute values for calculations and format the final result for reading. Optional rounding is a separate operation: it changes a value according to an explicitly chosen rule and application level. Showing fewer decimal places should never silently become that rule.

When you receive somebody else’s decimal total

Check the column heading and ask whether the value is a duration or a time of day. If the source has already rounded to a limited number of decimals, converting back may not recover the original minute count. Keep dated shift records when available; a single displayed decimal total cannot reconstruct start times, break intervals or the dates on which work occurred.

Sources and method

• NIST SP 330, Section 4, Table 8Time-unit definitions only; not a payroll authority or product endorsement.
• Original worked calculationSynthetic example data, explicit input rules and direct integer-minute arithmetic.