Rounding, precision and what a degree means
A degree is 60 arcminutes and an arcminute is 60 arcseconds. Precision in the tools is usually given to the arcminute or arcsecond, which is far finer than a human reading of a chart needs.
What it is
Rounding matters at boundaries: a planet at 29 degrees 59 minutes is in one sign and at 30 degrees 0 minutes in the next. The tools round for display only, and the calculation keeps the full value.
How it is worked out or read
A time error of one minute moves the Moon about 13 arcseconds, and a Lagna by a similar small amount. Errors of this size rarely change a result, except at a boundary.
Where it appears on this site
The units and rounding are stated in the method page. The birth time article explains the sensitivity of the Lagna.
What the numbers on screen mean
The tools on this site compute positions to many decimal places internally, but display them rounded: longitudes to the nearest minute of arc, and times to the nearest minute. Rounding makes results readable, but it means a displayed value can sit up to half a unit away from the computed one. In almost every case this has no effect on the reading.
When rounding matters
Rounding matters near boundaries. A planet shown at 29 degrees 59 minutes of a sign is still in that sign, but only just; a planet shown at 0 degrees 0 minutes may have entered the sign a few seconds before the moment computed. The same applies to nakshatra and pada boundaries and to tithi end times close to sunrise. When a value is this close to a boundary, the reader should treat the classification as uncertain, especially since the birth time itself is rarely known to the second.
The real limit: the inputs
The precision of the calculation is almost always far greater than the precision of the inputs. A birth time recorded to the nearest five minutes gives a Lagna uncertain by over a degree and a Moon uncertain by over two minutes of arc. Displaying positions to seconds of arc would therefore suggest a precision the chart does not have. Rounding to the minute is a deliberate choice that matches the realistic accuracy of most birth data.
False precision in readings
The same caution applies to interpretations. A dasha table that gives the start of a sub-period to the day can look very exact, but an error of a few minutes in birth time shifts every date by days or weeks. Divisional charts such as the D60 change every couple of minutes of birth time. A careful reader states results with a precision that matches the data, and avoids drawing firm conclusions from fine distinctions the birth time cannot support.
A practical rule
As a rule of thumb, treat any classification that would change with a shift of a degree in the Lagna, half a degree in the Moon or a few minutes in an end time as uncertain, and say so. This keeps the reading honest without discarding the useful information in the chart.