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Scientific Notation Multiplication Calculator

Work out scientific notation multiplication instantly with clear inputs, formula shown and shareable results.

About Scientific Notation Multiplication Calculator

Multiplying in standard form is easy: multiply the mantissas and add the exponents, then renormalise the mantissa back into the range 1 to 10.

Formula

Multiplying standard form

(a×10ⁿ)(b×10ᵐ) = ab × 10^(n+m), then renormalise

Worked example

With the default values below, Scientific Notation Multiplication Calculator returns Product in standard form of 1 × 10^6. Change any input above and every figure here is recalculated in your browser.

Inputs used

First mantissa
2.5
First exponent
8
Second mantissa
4
Second exponent
-3

Results

Product in standard form
1 × 10^6
Mantissa
1.00000000
Exponent
6
Ordinary number
1,000,000.000000

Step by step

  1. 1Values used
  2. 2Multiplying standard form
  3. 3Product in standard form= 1 × 10^6
  4. 4Mantissa= 1.00000000
  5. 5Exponent= 6
  6. 6Ordinary number= 1,000,000.000000

Assumptions and limits

  • The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

2.5 × 10⁸ times 4 × 10⁻³?

10 × 10⁵ = 1 × 10⁶, that is 1000000.

Why renormalise?

The mantissa product can reach up to 100, so shifting a power of ten keeps the answer in proper standard form.

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