Scientific Notation Converter
The ultimate tool for converting numbers. Supports Engineering Notation, E-Notation, and SI Prefixes.
Number Input
Accepts: Standard, Scientific, E-Notation
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Enter a number to see Scientific, Engineering, and SI formats instantly.
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Why Notation Matters
The universe operates on scales that defy standard numbers. From the width of a DNA helix to the distance between galaxies, zeros become a burden.
Scientific Notation is the language of scale. It compresses unwieldy strings of digits into a compact, standardized format: a coefficient multiplied by a power of 10. This not only saves space but makes arithmetic with massive or microscopic numbers manageable.
Engineering vs. Scientific
Coefficient must be between 1 and 10.
Example: 2.5 × 10⁴
Exponent must be a multiple of 3. Matches Metric prefixes (kilo, mega, etc).
Example: 25 × 10³ (25 k)
Real World Examples
- Speed of Light3.00 × 10⁸ m/s
- Avogadro6.022 × 10²³
- Electron Mass9.109 × 10⁻³¹ kg
- Proton Size8.41 × 10⁻¹⁶ m
Mastering Significant Figures
Precision is key in science. Trailing zeros in a number like "5200" are ambiguous—are there exactly 5200, or is it rounded to the nearest hundred?
Scientific notation eliminates this ambiguity.
- 5.2 × 10³ indicates 2 significant figures (precision to hundreds).
- 5.200 × 10³ indicates 4 significant figures (precision to ones).
Use the Precision Slider in this tool to adjust the output to match the precision of your original measurement. This ensures you aren't reporting false accuracy.
Frequently Asked Questions
What is scientific notation?
Scientific notation is a method of writing very large or very small numbers. It expresses a number as a product of a number between 1 and 10 (the coefficient) and a power of 10. For example, 500 becomes 5 × 10².
What is the difference between scientific and engineering notation?
In scientific notation, the coefficient is between 1 and 10. In engineering notation, the exponent is always a multiple of 3 (e.g., 10³, 10⁶, 10⁻⁹), allowing the number to align with SI prefixes like kilo, mega, and nano. The coefficient in engineering notation is strictly between 1 and 1000.
What is E notation?
E notation (or exponential notation) is a format commonly used in calculators and programming languages where "× 10^" is replaced by "E" or "e". For example, 6.02 × 10²³ is written as 6.02E23.
How do I convert standard notation to scientific notation manually?
Move the decimal point until you have a number between 1 and 10. Count the number of places you moved. If you moved left, the exponent is positive (large number). If you moved right, the exponent is negative (small number).
How to convert scientific notation to a decimal?
Move the decimal point of the coefficient to the right for positive exponents, or to the left for negative exponents, by the number of places indicated by the exponent.
Why do we use scientific notation?
It simplifies arithmetic operations (multiplication and division become adding/subtracting exponents) and makes it easier to read and communicate values like the speed of light or the mass of an electron without writing long strings of zeros.
What are significant figures?
Significant figures (sig figs) are the digits in a number that carry meaningful information about its precision. When converting to scientific notation, you typically keep only the significant digits in the coefficient.
Can negative numbers be written in scientific notation?
Yes. The sign belongs to the coefficient. For example, -0.005 is written as -5 × 10⁻³. The exponent sign indicates magnitude (small vs large), not positive/negative value.
What is 10 to the power of 0?
10⁰ equals 1. So, 5 × 10⁰ is simply 5.
How do I type exponents on a calculator?
Look for an "EE", "EXP", or "x10ⁿ" button. This enters the "× 10^" part automatically.
What is a normalized scientific notation?
Normalized means strictly adhering to the rule that the coefficient must be at least 1 but less than 10. 12 × 10² is not normalized; 1.2 × 10³ is.
Why use engineering notation?
It aligns directly with metric prefixes. A result of 25 × 10⁻⁶ immediately tells an engineer "25 micro-units", whereas 2.5 × 10⁻⁵ requires mental conversion.
How does this tool handle sig figs?
Our tool allows you to set the desired number of significant figures using the precision slider, automatically rounding the coefficient to your specification.
Is 0.5 x 10^3 scientific notation?
Technically no, because the coefficient (0.5) is less than 1. Correct scientific notation would be 5.0 × 10².
What is the order of magnitude?
The order of magnitude is usually the exponent in scientific notation, giving a rough sense of the "scale" of the number (e.g., thousands vs millions).