The numbers you see may not be the numbers used
A published number is often a shorter version of a more detailed value. A table might show one decimal place even though its calculations use several. That makes the table easier to read, but it can create a puzzle: adding the displayed parts may give a slightly different answer from the displayed total.
Imagine two values of 1.46. If each is shown to one decimal place, the table displays 1.5 and 1.5. Their displayed sum is 3.0. But the unrounded values add to 2.92, which appears as 2.9 when rounded to one decimal place. Neither displayed calculation is necessarily a mistake. The difference comes from rounding the parts separately from the total.
This distinction matters whenever you try to verify a chart, compare figures across reports or reuse a published table. Before assuming that a mismatch is an error, ask whether the figures shown are inputs to the calculation or rounded versions of its results.
Why percentages sometimes miss 100%
Percentages are especially likely to produce small rounding differences. Suppose three categories each represent exactly one-third of a whole. Rounded to one decimal place, each appears as 33.3%. Add the displayed percentages and you get 99.9%, although the underlying shares cover the entire whole.
The same effect can make displayed shares add to slightly more than 100%. It can also affect subtotals: a report may calculate a subtotal from underlying counts and round it, rather than add the already rounded percentages above it. If the categories overlap, however, their percentages may exceed 100% for a different reason. People could belong to more than one category, so the shares were never meant to form a single whole.
Check what the percentage means before judging the arithmetic. Look for the denominator, whether categories are mutually exclusive, and any note explaining the displayed precision. Rounding is a plausible explanation for a small gap; it is not a blanket explanation for every total that looks wrong.
Display precision is not measurement accuracy
Decimal places tell you how a number is presented, not necessarily how accurately it was measured. A value shown as 12.0 may come from careful measurement, a rough estimate or a calculation using assumptions. The extra zero alone cannot tell you which. Conversely, rounding a sound measurement to 12 may be entirely appropriate for a general explanation.
It helps to separate two questions. First, how much detail was retained in the displayed figure? Second, how reliable is the value behind it? Rounding addresses the first question. To consider the second, you need context about how the data was collected, defined or estimated. More digits cannot repair uncertain inputs.
Repeated calculations can make this distinction important. If you round an intermediate value and then use it in another calculation, the result may differ from one calculated with the unrounded value. When possible, keep the underlying precision through the calculation and round only the final result for display.
A practical way to check a mismatch
Start by comparing like with like: confirm that every figure uses the same unit, time period and set of categories. Then note how many decimal places are shown. If the difference is small relative to that level of rounding, try calculating from any available unrounded counts or values. Those underlying figures may explain why the printed parts and total differ.
If the gap remains substantial, inspect the definitions. A total might include an unlisted category, while a percentage might use a different denominator from the one you assumed. Also check whether a displayed figure is a subtotal, an average or a rate rather than a simple sum. These distinctions can matter more than the last decimal place.
Finally, describe what you found without implying more certainty than the table permits. You might say that displayed shares do not sum exactly to 100% and that independent rounding could explain the difference. If the available information is insufficient to resolve a larger discrepancy, treat it as an open question rather than silently adjusting a number to make the table add up.
