Convert To and From Scientific Notation
This free scientific notation calculator converts ordinary numbers into scientific notation and back again. Enter a number like 35,000 and get 3.5 x 104, or enter 3.5e4 and get 35,000. The tool above handles very large and very small numbers cleanly, which is exactly where scientific notation earns its keep — writing 0.00000045 as 4.5 x 10?7 is far easier to read and far less error-prone.
How to Use the Calculator
- Choose Number -> Scientific notation or Scientific notation -> Number.
- Type your value (for scientific notation, use “e” form such as 3.5e4).
- Press Convert.
What Scientific Notation Is
Scientific notation writes a number as a coefficient between 1 and 10 multiplied by a power of ten: a x 10n. The exponent n tells you how many places the decimal point moves. A positive exponent means a large number (move the point right): 6.02 x 1023 is a 6 followed by 23 digits. A negative exponent means a small number (move the point left): 1.6 x 10?19 is a tiny fraction. This compact form is the standard way scientists and engineers write quantities that would otherwise have dozens of zeros.
Worked Examples
35,000 becomes 3.5 x 104 because the decimal point moves four places left. 0.0042 becomes 4.2 x 10?3 because the point moves three places right. Going the other way, 2.5 x 106 expands to 2,500,000, and 9 x 10?5 expands to 0.00009. The calculator does the place-counting for you and shows the result in both the x 10n form and the plain number, so you can copy whichever you need.
Where It Is Used
Scientific notation appears throughout physics, chemistry, astronomy, biology, and engineering, where quantities span an enormous range — from the mass of an electron to the distance between galaxies. It is also how calculators and programming languages display numbers that are too big or too small to show normally (often using the “e” notation, like 1.23e-9). Students meet it in math and science classes, and converting fluently between the compact and expanded forms makes homework and lab work much faster.
Engineering Notation and the “e” Form
You will often see scientific notation written with an “e” instead of x 10, because that is what fits on a calculator screen or in code: 3.5 x 104 is typed as 3.5e4, and 4.5 x 10?7 as 4.5e-7. A close relative, engineering notation, restricts the exponent to multiples of three (so it lines up with units like kilo, mega, and micro). This converter focuses on standard scientific notation, accepting the everyday “e” form on input so you can paste values straight from a calculator or spreadsheet.
Frequently Asked Questions
How do I write a number in scientific notation?
Move the decimal point so one non-zero digit is in front of it, then multiply by 10 raised to the number of places you moved. The tool does this automatically.
What does 1e6 mean?
1e6 is 1 x 106, which equals 1,000,000.
Is the scientific notation calculator free?
Yes — free, browser-based, and no signup required.
Working With Numbers in Scientific Notation
Scientific notation does more than shorten long numbers — it makes calculations with very large or very small values manageable. To multiply two numbers in scientific notation, multiply the coefficients and add the exponents: (3 × 10^4) × (2 × 10^3) = 6 × 10^7. To divide, divide the coefficients and subtract the exponents. To add or subtract, the exponents must match first, so you rewrite one number until both share the same power of ten, then combine the coefficients. These rules are exactly why scientists adopted the notation: it keeps the arithmetic simple even when the numbers span dozens of zeros.
Significant Figures and Precision
Scientific notation also makes significant figures clear. Writing 4,500 as 4.5 × 10^3 shows two significant figures, while 4.50 × 10^3 shows three — a distinction that is invisible in the plain number but important in science and engineering, where precision must be reported honestly. When you convert a measured value into scientific notation, the coefficient should carry only the digits you actually know. This is why lab reports, physics homework, and technical specifications lean on the notation: it communicates both the size of a quantity and how precisely it was measured, all in a compact form the calculator above produces instantly.