Scientific Notation Calculator - Convert to Standard Form
Convert any number to scientific notation or expand scientific notation back to standard decimal form — instantly and accurately.
Choose a conversion direction, enter your number or coefficient and exponent, then click Calculate for the result with full notation.
Scientific Notation Calculator - Convert to Standard Form
Convert any number to scientific notation or expand scientific notation back to standard decimal form — instantly and accurately.
About the scientific notation calculator
Scientific notation is a compact way of writing very large or very small numbers using a coefficient multiplied by a power of ten. A number in standard scientific notation takes the form a × 10ⁿ, where a (the coefficient) is a number with one non-zero digit to the left of the decimal point (i.e., 1 ≤ |a| < 10), and n (the exponent) is an integer. For example, the speed of light in a vacuum is approximately 299,792,458 metres per second — expressed in scientific notation this is 2.99792458 × 10⁸ m/s. Similarly, the mass of an electron is about 9.109 × 10⁻³¹ kg.
Scientific notation is indispensable in physics, chemistry, astronomy, engineering, and biology because many natural constants and measurements span an enormous range of magnitudes. Writing 0.00000000000000000000000166054 kg (the mass of a proton in kilograms) is error-prone; 1.66054 × 10⁻²⁴ kg communicates the magnitude immediately. Scientific notation also makes arithmetic with very large or small numbers more systematic: to multiply two numbers in scientific notation, multiply the coefficients and add the exponents; to divide, divide the coefficients and subtract the exponents.
This calculator supports two conversion directions. In Decimal → Scientific Notation mode, you enter any decimal number and the tool identifies the exponent n (the integer part of log₁₀(|x|)) and divides the number by 10ⁿ to get the coefficient a. In Scientific Notation → Decimal mode, you enter the coefficient a and the exponent n, and the tool multiplies a by 10ⁿ to produce the decimal expansion.
A closely related notation is engineering notation, in which the exponent is always a multiple of 3, so that the coefficient falls between 1 and 999. This corresponds to standard SI prefixes: 10³ = kilo, 10⁶ = mega, 10⁹ = giga, 10⁻³ = milli, 10⁻⁶ = micro, 10⁻⁹ = nano. While this calculator uses standard scientific notation (coefficient between 1 and 10), the results can be easily converted to engineering notation by adjusting the exponent to the nearest multiple of 3 and scaling the coefficient accordingly.
Whether you are a student converting measurements for a chemistry lab, a programmer working with floating-point number representations, or an engineer checking that a calculated value is in the right order of magnitude, this scientific notation calculator gives you instant, accurate conversions in both directions.
Scientific notation examples
Conversions in both directions — decimal to scientific and scientific to decimal.
| Input | Result | Notes |
|---|---|---|
| 6,500,000 | 6.5 × 10⁶ | The coefficient is 6.5 (between 1 and 10) and the exponent is 6. Used in astronomy: 6.5 million light-years, etc. |
| 0.000034 | 3.4 × 10⁻⁵ | Negative exponent indicates a small number. The decimal point moves 5 places to the right to get the coefficient 3.4. |
| 3.4 × 10⁻⁵ | 0.000034 | Reverse conversion: multiplying 3.4 by 10⁻⁵ moves the decimal 5 places left. |
| 9,109,000 | 9.109 × 10⁶ | Approximation of 9.109 million. Coefficient rounded to 4 significant figures. |
How to use the scientific notation calculator
- Select the conversion direction: 'Decimal → Scientific Notation' to convert a plain number, or 'Scientific Notation → Decimal' to expand a scientific expression.
- For Decimal → Scientific Notation: type any number (e.g., 0.000034 or 6500000) into the Decimal Number field.
- For Scientific Notation → Decimal: enter the coefficient a (e.g., 3.4) and the integer exponent n (e.g., −5) in their respective fields.
- Click Calculate to see the converted result displayed with superscript exponent notation.
- Click Reset to clear all fields and start a new conversion.
Scientific notation FAQ
What is scientific notation?
Scientific notation is a way of expressing numbers as a product of a coefficient (between 1 and 10) and a power of ten — written as a × 10ⁿ. It makes very large and very small numbers easier to write, compare, and use in calculations. For example, 93,000,000 miles (the average Earth–Sun distance) is written 9.3 × 10⁷ miles.
How do I convert a number to scientific notation?
Move the decimal point until the number has exactly one non-zero digit to its left. Count how many places you moved the point: this count becomes the exponent n. If you moved left, n is positive; if you moved right (for small numbers), n is negative. The resulting number is your coefficient a.
How do I convert scientific notation back to decimal?
Multiply the coefficient by 10 raised to the exponent. For 3.4 × 10⁻⁵, compute 3.4 ÷ 100,000 = 0.000034. Equivalently, move the decimal point in the coefficient to the right (positive exponent) or left (negative exponent) by the number of places equal to the absolute value of the exponent.
What is the difference between scientific and engineering notation?
In scientific notation, the exponent can be any integer and the coefficient is between 1 and 10. In engineering notation, the exponent is always a multiple of 3 (…, −6, −3, 0, 3, 6, …) so that the coefficient ranges from 1 to 999. Engineering notation aligns with SI metric prefixes: 10³ = kilo, 10⁶ = mega, 10⁻³ = milli, etc.
How do I multiply numbers in scientific notation?
Multiply the coefficients and add the exponents. For example, (2.5 × 10³) × (4.0 × 10²) = (2.5 × 4.0) × 10^(3+2) = 10.0 × 10⁵ = 1.0 × 10⁶. If the product of the coefficients is ≥ 10, adjust by increasing the exponent by 1 and dividing the coefficient by 10.
Can the coefficient be negative?
Yes. For negative numbers, the coefficient is negative. For example, −45,000 in scientific notation is −4.5 × 10⁴. The sign belongs to the coefficient, not the exponent. The exponent only encodes the order of magnitude.