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Category Math & Algebra

Enter a Number Accepts plain numbers or scientific notation (e.g., 3.5e8, 2.1×10^-4)

Target Exponent

Integer power of 10 for the result

Presets:

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About

Scientific notation expresses any real number as m × 10^e, where the mantissa m satisfies 1 ≤ |m| < 10 and e is an integer exponent. Changing the exponent without changing the value requires compensating the mantissa: setting a new exponent e₂ means the mantissa must shift by a factor of 10^{e₁ − e₂}. This operation is routine in physics, engineering, and chemistry where aligning exponents is required before adding quantities or matching unit prefixes. Errors in manual re-expression - especially sign mistakes in the exponent delta - propagate silently through calculations and have caused specification mismatches in semiconductor fabrication and dosimetry. This tool performs the conversion exactly, preserving up to 20 significant digits.

Formulas

Given a number N expressed as m₁ × 10^e₁, to re-express it with a new exponent e₂:

m₂ = m₁ × 10^{(e₁ − e₂)}

The resulting representation is:

N = m₂ × 10^e₂

Where m₁ is the original mantissa (coefficient). e₁ is the original exponent (power of 10). e₂ is the target exponent chosen by the user. m₂ is the new mantissa that preserves the original value. The identity holds because 10^{e₁ − e₂} × 10^e₂ = 10^e₁. For normalization to standard scientific notation, e₂ is chosen so that 1 ≤ |m₂| < 10.

Reference Data

SI Prefix	Symbol	Exponent	Factor	Example Usage
Quetta	Q	30	10³⁰	Cosmic distances
Ronna	R	27	10²⁷	Galactic masses
Yotta	Y	24	10²⁴	Data volumes (future)
Zetta	Z	21	10²¹	Global internet traffic
Exa	E	18	10¹⁸	Exabytes of storage
Peta	P	15	10¹⁵	Petaflops computing
Tera	T	12	10¹²	Terabytes, frequencies
Giga	G	9	10⁹	GHz clock speeds
Mega	M	6	10⁶	Megapascals, MHz
Kilo	k	3	10³	Kilograms, kilometers
Hecto	h	2	10²	Hectopascals (weather)
Deca	da	1	10¹	Decameters
(base)	-	0	10⁰	Meters, grams, seconds
Deci	d	−1	10⁻¹	Decibels, deciliters
Centi	c	−2	10⁻²	Centimeters
Milli	m	−3	10⁻³	Milliamps, millimeters
Micro	µ	−6	10⁻⁶	Microfarads, microns
Nano	n	−9	10⁻⁹	Nanometers, nanoseconds
Pico	p	−12	10⁻¹²	Picofarads
Femto	f	−15	10⁻¹⁵	Femtosecond lasers
Atto	a	−18	10⁻¹⁸	Attosecond physics
Zepto	z	−21	10⁻²¹	Particle cross-sections
Yocto	y	−24	10⁻²⁴	Atomic-scale masses
Ronto	r	−27	10⁻²⁷	Subatomic masses
Quecto	q	−30	10⁻³⁰	Quantum phenomena

Frequently Asked Questions

The tool preserves up to 20 significant digits using JavaScript's native Number precision (IEEE 754 double, ~15-17 significant decimal digits). If you input a number with more than 17 significant digits, the least significant digits may be rounded. For most scientific and engineering work, this exceeds required precision.

Yes. The parser accepts standard scientific notation (3.5e8, 3.5E8, 3.5×10^8, 3.5e-12). It also accepts plain decimal numbers like 0.00042 or 350000. The tool auto-detects the current normalized exponent from the input.

Engineering notation uses exponents that are multiples of 3 (matching SI prefixes like kilo, mega, micro). In some fields, aligning exponents across multiple quantities enables direct comparison or addition of mantissas. For instance, when adding 3.2 × 10^5 and 7.1 × 10^3, converting both to exponent 3 gives 320 × 10^3 + 7.1 × 10^3 = 327.1 × 10^3.

Zero is handled as a special case: 0 × 10^e for any exponent e. Negative numbers preserve their sign in the mantissa. The tool handles values up to approximately ±1.7976931348623157 × 10^308 (JavaScript's Number.MAX_VALUE) and as small as ±5 × 10^-324 (Number.MIN_VALUE). Infinity and NaN inputs trigger an error toast.

Normalized scientific notation constrains the mantissa so that 1 ≤ |m| < 10, yielding a unique representation. Denormalized notation allows any mantissa with any exponent, which is what this tool produces when you choose a custom exponent. Both are mathematically valid representations of the same value.