Behind the result - No mystery in the method
Each pair means (coefficient) × 10^(entered exponent). Coefficients can be non-normalized and can themselves use e notation. Addition and subtraction align to the larger entered power before combining coefficients. Multiplication combines coefficients and adds powers; division divides coefficients and subtracts powers. Reduced integer fractions keep intermediate values exact. The final nonzero coefficient is normalized. A reduced denominator containing only factors 2 and 5 gives an exact terminating decimal; other denominators give an exact fraction plus a rounded scientific display. The selected precision applies only to repeating displays, not to already exact finite results. Measurement significant-figure rules are not automatically imposed.
This tool does not store inputs, fetch live data or replace a teacher or textbook explanation. Blank optional fields are omitted. Text is displayed literally, not interpreted as HTML.
Changing an input clears the old answer so it cannot be mistaken for the new calculation. Download text makes a local copy of the current working. Print / Save PDF uses the browser’s print controls. Review any note before sharing.
Before you go
Is an answer such as one divided by three exact?
The reduced fraction 1 / 3 is exact. Its decimal does not terminate, so the scientific display is rounded to your chosen 1–30 significant figures. The result labels this distinction and uses half-away-from-zero rounding.
Why do add and multiply show different steps?
Addition and subtraction need a common power of ten so their coefficients refer to the same place value. Multiplication adds exponents and division subtracts them. Every nonzero final answer is then normalized to a coefficient magnitude in [1, 10).
Does this apply laboratory significant-figure rules?
No. It performs exact arithmetic on the values entered. The repeating-display precision is a formatting choice, not an uncertainty analysis. Use your course rules and the separate rounding tool to decide what should be reported.
Can I divide by zero or share my working?
Division by zero is rejected rather than displayed as infinity. Valid results can be downloaded as text or printed with their working, entered values and rounding explanation. No server-side answer history is created.