Multiply Two or More Numbers

Formula and method

Multiply the entered factors together. An entered zero makes the product zero, while blank optional factors are omitted. In two-factor mode, divide a known product by a nonzero known factor to recover the other.

P = a × b; for multiple factors, P = a₁ × a₂ × ⋯ × aₙ.

Worked example

Enter these known values and leave the other values blank.

Assumptions and limitations

• The two-factor mode retains editable product and factor controls, including both source inverse directions. Dividing by a zero factor cannot determine a unique missing factor.
• Many-factor mode supports two through ten entered real factors. The slot selector opens three through ten fields; filled higher slots remain visible even if a smaller count is selected. Blanks are omitted and an entered zero is a real factor.
• Switching modes retains original values. The two-factor product uses the first two factors; the many-factor product uses every entered factor among the ten retained controls.
• Each factor is zero or finite magnitude1e-10000 through1e10000. A two-factor result is zero or finite magnitude1e-20000 through1e20000. Decimal arithmetic uses64-digit working precision.
• The worked explanation identifies the entered factors and their product. The original callback rounding ceiling is replaced by relative rounding; finite nonzero tiny values remain visible in scientific notation.
• Inputs accept decimal or e notation and bounded arithmetic expressions only when each intermediate and final value can be verified exactly as a finite decimal. Repeating fractions, functions, symbols and expressions that lose digits are rejected with guidance. Enter their finite decimal value instead; the calculator-specific magnitude and precision limits still apply.

Common questions

References

• Captured multiplication controls and equation

Preserve the captured two-factor multiplication equation and both inverse directions. Translate only the captured many-factor callback to a local decimal product of entered factors; omit blanks, preserve zeros/signs and require at least two known factors. Promote its numeric export to a readonly result and retain the original conditional explanation. Repair its15-decimal-place rounding ceiling with relative presentation precision and scientific fallback for small nonzero products. No captured JavaScript is evaluated by product code. Bind optional many-factor multiplication to the complete captured source and complete raw/authored compiled schemas only. Preserve both modes, all eight factor-slot choices, all thirteen original controls, every lock/default and all three original equation directions. Entered factors are zero or finite magnitude1e-10000 through1e10000; the two-factor result is zero or finite magnitude1e-20000 through1e20000. Retained filled factor slots remain visible when their count selector is reduced. Solve either factor only when the other factor is nonzero; a zero-factor inverse can remain undetermined. Use exact-sign note conditions for negative parentheses and format the many-factor numeric result without changing its value. Preserve finite nonzero source values with the source-specific scientific display policy.

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