About

Accuracy is the primary constraint in scientific data entry and financial accounting. Standard floating-point arithmetic (IEEE 754) often introduces microscopic errors-such as 0.1 × 0.2 resulting in 0.020000000000000004. While negligible in casual use, these artifacts can compound significantly in large datasets.

This tool bypasses standard browser math by treating inputs as precise strings. It guarantees exact decimal placement up to 20 places, ensuring that the Law of Significant Figures is respected. It also bridges the gap between digital representation and arithmetic theory by providing the fractional equivalent of the result, useful for exact symbolic computation.

Formulas

The calculation maintains precision by determining the scale of each number (powers of 10):

x = a × 10^m, y = b × 10ⁿ

Product = (x × y) / 10^(m+n)

For fraction conversion, the result R is expressed as:

R = Integer(R × 10^k)10^k

This fraction is then reduced by dividing the numerator and denominator by their Greatest Common Divisor (GCD).

Reference Data

Input A	Input B	Precise Result	Fraction
0.5	0.5	0.25	14
0.1	0.1	0.01	1100
2.5	2.5	6.25	254
0.125	8	1.0	11
0.33	3	0.99	99100
1.5	1.5	2.25	94
0.001	1000	1.0	11
5.5	2	11.0	111

Frequently Asked Questions

It is designed to be arbitrary-precision for standard inputs, avoiding the floating-point errors found in standard JavaScript or Excel calculations.

The tool uses standard rounding (Round Half Up). For example, rounding 1.255 to 2 decimal places results in 1.26.

Yes. The standard rules of signs apply: negative × negative = positive, positive × negative = negative.

Fractions are often preferred in algebra and engineering because they are exact representations of value, whereas decimals can sometimes be approximations (like 0.333...).