What is scientific notation?

A way to write very large or small numbers: x = a × 10ᵇ, where 1 ≤ |a| < 10. Example: 5,900,000 = 5.9 × 10⁶.

How do I multiply two numbers in scientific notation?

Multiply the mantissas and add the exponents: (a × 10ᵐ) × (b × 10ⁿ) = ab × 10ᵐ⁺ⁿ. Then normalise if |ab| ≥ 10.

What is the difference between scientific and standard notation?

Standard notation is the familiar decimal form (e.g. 5,900,000). Scientific notation compresses it to 5.9 × 10⁶ for readability and calculation.

Scientific Notation Calculator

Q: How do I multiply two numbers in scientific notation?

Multiply the mantissas and add the exponents: (a × 10ᵐ) × (b × 10ⁿ) = ab × 10ᵐ⁺ⁿ. Then normalise if |ab| ≥ 10.

Q: What is the difference between scientific and standard notation?

Standard notation is the familiar decimal form (e.g. 5,900,000). Scientific notation compresses it to 5.9 × 10⁶ for readability and calculation.

Enter any decimal or large number to convert it to scientific notation (a × 10ᵇ), or perform arithmetic operations on two numbers already in scientific notation.

How to use this calculator

Select 'Convert' to turn any number into scientific and engineering notation.
Select 'Arithmetic' to add, subtract, multiply, or divide two numbers already given as a × 10ᵇ.
Results are automatically expressed in normalised scientific notation.

Formula & method

Scientific notation conversion

x = a × 10ᵇ where 1 ≤ |a| < 10 · Multiplication: (a × 10ᵐ) × (b × 10ⁿ) = ab × 10ᵐ⁺ⁿ

a = mantissa (coefficient), b = exponent (order of magnitude).

Example

1,234,567.89 → 1.2346 × 10⁶. Multiplication: (1.5 × 10⁶) × (2 × 10³) = 3.0 × 10⁹.

Key insights

Scientific notation requires 1 ≤ |a| < 10 for the mantissa. In engineering notation, exponents are always multiples of 3.
Very large numbers (e.g. Avogadro's number 6.022 × 10²³) and very small ones (e.g. electron mass 9.109 × 10⁻³¹ kg) are standard applications.
Multiplying in scientific notation: (a × 10ᵐ)(b × 10ⁿ) = ab × 10ᵐ⁺ⁿ.
Adding/subtracting requires aligning exponents first before combining mantissas.

How to interpret your result

Scientific vs engineering notation

Scientific notation has mantissa 1 ≤ |a| < 10. Engineering notation keeps exponents as multiples of 3, matching SI prefixes (kilo, mega, giga).

E-notation

Scientific calculators and programming languages often write 1.5e6 for 1.5 × 10⁶.

Frequently asked questions

What is scientific notation?: A way to write very large or small numbers: x = a × 10ᵇ, where 1 ≤ |a| < 10. Example: 5,900,000 = 5.9 × 10⁶.
How do I multiply two numbers in scientific notation?: Multiply the mantissas and add the exponents: (a × 10ᵐ) × (b × 10ⁿ) = ab × 10ᵐ⁺ⁿ. Then normalise if |ab| ≥ 10.
What is the difference between scientific and standard notation?: Standard notation is the familiar decimal form (e.g. 5,900,000). Scientific notation compresses it to 5.9 × 10⁶ for readability and calculation.

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