It is a way to write numbers as a × 10ⁿ, where the coefficient a is between 1 and 10 (in absolute value) and n is an integer (positive, negative or zero).
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Convert between decimal and scientific notation (a × 10ⁿ) in both directions.
Scientific notation represents numbers as a × 10ⁿ, where the coefficient satisfies 1 ≤ |a| < 10 and n is an integer. It is used in science, engineering and mathematics to write very large numbers (like 6.022 × 10²³) or very small ones (like 1.6 × 10⁻¹⁹) without a long string of zeros. This tool works in both directions and accepts input in three formats: plain decimal (32000), programming E-notation (3.2e4) and the mathematical a×10^b notation (3.2×10^4). To find the exponent it computes n = floor(log₁₀|x|) and the coefficient a = x ÷ 10ⁿ, normalizing the result so a lands in the canonical range [1, 10), if rounding pushes a to 10, the exponent goes up by 1. The coefficient is shown with up to 10 significant digits and the math uses 64-bit floating point, which covers values up to about 1.8 × 10³⁰⁸; beyond that the tool warns the number is out of range. Everything runs locally in your browser.
To bring a decimal number to the form a × 10ⁿ, the tool first determines the exponent with n = floor(log₁₀ of the absolute value): it is the number of places separating the most significant digit from the units position. It then gets the coefficient by dividing the number by 10ⁿ, which always leaves a with a single digit before the decimal point.
The form is unique because we require 1 ≤ |a| < 10. Numbers larger than 1 have a positive exponent (the point moves left when normalizing); numbers between 0 and 1 have a negative exponent (the point moves right). Going the other way, multiplying by 10ⁿ simply shifts the decimal point n places: right if n is positive, left if it is negative.
Example 1, decimal to scientific: 93,000,000. The exponent is floor(log₁₀ 93,000,000) = floor(7.968) = 7, and the coefficient is 93,000,000 ÷ 10⁷ = 9.3. Result: 9.3 × 10⁷.
Example 2, scientific to decimal: 2.99 × 10⁸. The exponent 8 shifts the decimal point eight places to the right from the coefficient, turning 2.99 into 299,000,000 (close to the speed of light, ~2.99 × 10⁸ m/s).
Do not confuse scientific notation with engineering notation: in scientific notation the coefficient stays in [1, 10); in engineering notation the exponent is always a multiple of 3 (to match kilo, mega, milli, micro) and the coefficient can go up to 999. Here we use the canonical scientific form, so 32 × 10² is rewritten as 3.2 × 10³. The coefficient is rounded to at most 10 significant digits, and values outside the float64 range (above ~1.8 × 10³⁰⁸) are rejected.
The notation shines when numbers escape human scale: Avogadro's constant (6.022 × 10²³), the electron charge (1.6 × 10⁻¹⁹ C), astronomical distances or the mass of a bacterium. Writing them this way makes it easy to compare orders of magnitude (just look at the exponent) and to multiply or divide by adding or subtracting exponents.
Paste the code into your HTML and the tool shows up on your page, without J-Kit's navigation and ads. It still runs in the browser of whoever visits your site.
<iframe
src="https://jkit.tools/embed/en-US/scientific-notation-converter"
width="100%"
height="600"
style="border:0"
loading="lazy"
title="Scientific Notation Converter"
></iframe>These references help contextualize formulas, standards, APIs and limitations used on this page. They do not replace professional validation when a result has legal, financial, medical or operational impact.
It is a way to write numbers as a × 10ⁿ, where the coefficient a is between 1 and 10 (in absolute value) and n is an integer (positive, negative or zero).
All calculations stay in your browser. No data is sent to any server.