Add, subtract, multiply, or divide two decimal numbers, with a clear explanation of how the decimal point is placed in the result.
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Decimal numbers extend the whole-number system with a decimal point to represent fractional parts, and the four basic arithmetic operations each follow their own rule for how that decimal point behaves in the result. For addition and subtraction, the numbers must conceptually be aligned by their decimal point (as if lining up columns), and the result naturally keeps as many decimal places as the input with the most decimal places. For multiplication, the total number of decimal places in the result equals the sum of the decimal places in both numbers being multiplied, before any trailing zeros are removed — for example, 1.2 (1 decimal place) times 0.03 (2 decimal places) produces a result with 3 decimal places. Division does not follow a similarly simple fixed rule, since the result can have far more decimal places than either input, or even repeat infinitely, which is why this calculator computes it directly rather than trying to predict decimal placement in advance. Floating-point rounding artifacts that sometimes appear in browser-based arithmetic (like 0.30000000000000004 instead of 0.3) are automatically cleaned up before the result is displayed.
Decimal arithmetic looks like an extension of whole-number arithmetic, and mostly it is — except that each of the four basic operations handles the decimal point according to its own distinct logic, and mixing those rules up is a common source of avoidable mistakes.
Addition and subtraction are the most intuitive: line the numbers up by their decimal points, as if stacking them in columns, and add or subtract normally. The number of decimal places in the result simply matches whichever input had more decimal places — adding 3.4 and 2.15 gives 5.55, taking on the two decimal places from the more precise input rather than the one decimal place from the less precise one.
Multiplication works differently, and this is where many people get tripped up. The number of decimal places in the raw product equals the sum of the decimal places in both factors, not the maximum. Multiplying 1.2 (one decimal place) by 0.03 (two decimal places) produces a result with three decimal places: 0.036. This rule holds regardless of how many digits appear before the decimal point — only the count of digits after it matters for predicting the product's decimal length.
Division breaks this pattern entirely. There is no simple formula that predicts how many decimal places a quotient will have just from the decimal places of the dividend and divisor. Dividing 1 by 4 gives exactly two decimal places (0.25), but dividing 1 by 3 produces a decimal that repeats forever (0.333...). This is precisely why decimal division is typically computed directly rather than estimated from a placement rule the way multiplication can be.
One practical wrinkle specific to computers and browsers is floating-point representation: because computers store decimal numbers in binary internally, some decimal values cannot be represented with perfect precision, occasionally producing results like 0.30000000000000004 instead of the expected 0.3. This is a well-known characteristic of how floating-point numbers work in virtually all programming languages, not a calculation error, and this tool rounds away that tiny residual imprecision before displaying a result, so what's shown matches the mathematically correct answer.
Because the total number of decimal places in a product equals the sum of the decimal places in both factors — multiplying a number with 2 decimal places by one with 3 decimal places produces up to 5 decimal places in the raw result, before any trailing zeros are trimmed.
Because dividing decimal numbers can produce a result with far more decimal places than either input — including results that repeat infinitely, like 1 ÷ 3 = 0.333... — so there's no simple formula to predict the result's decimal length in advance.
Very small floating-point rounding artifacts are cleaned up automatically (rounded to 10 decimal places) to avoid displaying results like 0.30000000000000004 instead of 0.3, but otherwise the full calculated result is shown.