Why an exact answer and a decimal can look different
Fractions, rounding, and the small details that matter when reading a result.
Exact values preserve the relationship
The fraction 1/3 is an exact value. A display such as 0.3333333333 stops after a finite number of digits, so it is an approximation. More digits may be useful, but they do not make a truncated decimal identical to the fraction.
Two arithmetic approaches on this site
The integer, reciprocal, squaring, and four-function tools use exact fraction arithmetic. The decimal-addition tool uses scaled whole numbers. Most graphing, statistical, and financial tools use floating-point calculations and round the display. Their pages explain the relevant limitations.
Do not round every intermediate step
Rounding intermediate values repeatedly can compound the error. Keep the full calculation internally and round the final presentation to a useful number of places. This matters particularly when subtracting nearly equal values or solving poorly scaled equations.
Choose precision for the task
A duration rounded to milliseconds is usually more readable than dozens of decimal places. A financial projection displayed to cents is still uncertain because its assumptions are uncertain. A precise-looking number is not evidence that a forecast is reliable.
Try the Adding Decimals Calculator with 0.1 and 0.2, then compare exact fractions in the Reciprocal Calculator.