How this calculator works
Multiply the received decimal coefficients as exact integers with decimal scales, then add the external exponents. Move the decimal point so the non-zero coefficient has magnitude at least one and below ten. Optional rounding happens once, half away from zero, and a rounded coefficient of ten raises the exponent again. The exponent remains separate, so products such as 6e2000 are supported without floating-point overflow. Numeric inputs can already have lost digits before calculation; trailing zeros are preserved only when you request significant figures.
Formula
(a×10^p)(b×10^q)=(ab)×10^(p+q). Normalize ab=c×10^k to obtain c×10^(p+q+k).
Worked example
(2.5×10³)(4×10⁻²)=10×10¹=1×10². Also (-6×10⁻⁵)(3×10²)=-18×10⁻³=-1.8×10⁻². Rounding 9.99 to two significant figures gives 1.0×10¹.
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Frequently asked questions
Must each entered coefficient be between one and ten?
No. The normalization step handles any finite coefficient, including negative values and zero.
How do I choose significant figures?
Choose the requested precision explicitly. For measured multiplication it is usually the fewest significant figures among the factors.
Why is there no expanded decimal readout?
Keeping coefficient and exponent separate makes very large and very small products readable and avoids overflow.