Scientific Notation Addition Calculator

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

About Scientific Notation Addition Calculator

To add numbers in standard form you must first give them the same exponent, add the mantissas, then renormalise so the mantissa lies between 1 and 10.

Formula

Adding standard form

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

Worked example

With the default values below, Scientific Notation Addition Calculator returns Sum in standard form of 3.65 × 10^5. Change any input above and every figure here is recalculated in your browser.

Inputs used

First mantissa: 3.2
First exponent: 5
Second mantissa: 4.5
Second exponent: 4

Results

Sum in standard form: 3.65 × 10^5
Mantissa: 3.65000000
Exponent: 5
Ordinary number: 365,000.000000

Step by step

1Values used
2Adding standard form
3Sum in standard form= 3.65 × 10^5
4Mantissa= 3.65000000
5Exponent= 5
6Ordinary number= 365,000.000000

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

3.2 × 10⁵ + 4.5 × 10⁴?

320000 + 45000 = 365000 = 3.65 × 10⁵.

Why can't I just add the mantissas?

Because they refer to different place values. Matching the exponents first is essential.