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m × 10ⁿ, with 1 ≤ |m| < 10

Scientific notation converter

Enter any number in plain, scientific or engineering form. The page returns all three, the significant figures and the number in words.

Both “0.00042” and “4.2e-4” are accepted and give the same answer.

Short answer: 0.00042 is 4.2 × 10⁻⁴ in scientific notation and420 × 10⁻⁶ in engineering notation. 12,345 is 1.2345 × 10⁴, or 12.345 × 10³.

When each form is used

Scientific notation normalises the mantissa so numbers can be compared at a glance; engineering notation keeps the exponent in threes so it maps onto kilo, mega, milli and micro. A physics paper uses the first, a datasheet usually the second.

Worked example

Avogadro’s number, 602214076000000000000000, is 6.02214076 × 10²³. In engineering form that is 602.214076 × 10²¹, which is why the SI prefix version reads 602 zetta rather than 6.02 × 10²³.

Scientific notation questions

What is scientific notation?

A number written as m × 10ⁿ with the mantissa m between 1 and 10. The speed of light is 3 × 10⁸ m/s and a hydrogen atom is 5.3 × 10⁻¹¹ m wide; the form exists so very large and very small values stay readable.

What is engineering notation?

The same idea with the exponent restricted to multiples of three, so the mantissa can be up to 999. It lines up with SI prefixes: 4.7 × 10³ is 4.7 k, and 2.2 × 10⁻⁶ is 2.2 µ. Both forms are shown because engineering work uses the second.

Does it lose precision?

No. The mantissa is computed from the exact double and shown with ten significant digits, so 6.02214076 × 10²³ comes back as 6.02214076 × 10²³ and not 6.02 × 10²³. No rounding happens between the two forms.

How do I read a negative exponent?

It counts places to the right of the decimal point: 10⁻³ is 0.001. In decimal form that is a shift towards zero, which is why a negative exponent usually means a very small quantity rather than a negative one.

Related tools

Logarithm calculatorThe exponent behind the notation.Number base converterBinary, octal, hex and base 36.Unit converterSI prefixes in physical units.