A worked example: multiplying two big numbers, then converting the result
Multiply 987654321098765432109876543210 by 123456789 in the big number calculator and the exact result is 121932631124828532112482853211126352690 — a 39-digit string with no rounding. Reading that many digits at a glance is hard, so taking that exact same digit string and entering it as the value in the scientific notation calculator, with the "Decimal to Scientific notation" direction, produces 1.2193263112482853211248285321112635269 × 10^38. Nothing was re-approximated in the handoff — the scientific notation calculator's mantissa reproduces every digit of the original product, just repositioned around a single power-of-ten exponent.
The formula: chaining big-integer output into scientific notation
The big number calculator's result field is already a plain digit string, which is exactly the input format the scientific notation calculator's value field expects — so the exact output of one becomes the exact input of the other with no conversion step in between. The scientific notation calculator then applies its usual a × 10^b decomposition to that string using arbitrary-precision decimal arithmetic, so a 39-digit input becomes a 39-significant-digit mantissa rather than being truncated to a handful of digits the way a typical calculator's display would.
A worked example: a 47-digit product simplified into scientific notation
The same chain works at even larger scale. Multiplying 78901234567890123456789012345678901234567890 by 56789 in the big number calculator gives the exact 51-digit result 4480722209875912220987591222098759122209875905210. Passing that digit string into the scientific notation calculator returns 4.48072220987591222098759122209875912220987590521 × 10^48 — the full 51-digit product compressed into a mantissa and an exponent of 48, still without dropping a single digit.
Why converting exact results to scientific notation matters
Big-integer arithmetic is exact precisely because it never rounds, but that same exactness is what makes its output unwieldy to read once a result stretches past a dozen or so digits. Converting that exact digit string to scientific notation keeps every digit of precision in the mantissa while making the overall magnitude — the exponent — instantly legible, which is the whole reason astronomy, chemistry, and other fields that produce enormous exact quantities report them in scientific notation rather than as raw digit strings.