Scientific notation writes a number as a coefficient between 1 and 10 times a power of ten, so 602,200,000,000,000,000,000,000 becomes 6.022 × 10²³. Type a plain number or a value already in notation and this tool shows every common form — standard decimal, scientific, E notation and engineering notation — at once.
Accepts plain numbers, E notation (1.5e3) and "a × 10^n". A comma works as a decimal point.
Enter a number to see every notation.
How it works
Whatever you type is first read as a single numeric value. It accepts a plain decimal (1500 or 0.00042), E notation (1.5e3), and the written form with a multiplication sign and a power of ten (1.5 × 10^3, 1.5 x 10^3 or 3*10^2). A decimal comma works too, so 3,14 is understood as 3.14.
From that value the tool finds the normalised coefficient by moving the decimal point until one non-zero digit sits in front of it; the number of places moved is the exponent. Moving left gives a positive exponent (large numbers), moving right gives a negative one (small numbers). Engineering notation is the same idea but the exponent is locked to a multiple of three, matching the SI prefixes kilo, mega, milli and micro.
Practical examples
A very large number
Enter 602200000000000000000000 — Avogadro’s number. It becomes 6.022 × 10²³ in scientific notation and 602.2 × 10²¹ in engineering notation, far easier to read and compare.
A very small number
The width of a hydrogen atom is about 0.0000000001 m. Entered as 0.0000000001, it converts to 1 × 10⁻¹⁰ and, in engineering form, 100 × 10⁻¹² — that is 100 picometres.
Expanding notation to a decimal
Paste 1.5 × 10^3 (or 1.5e3) and the tool expands it to the plain number 1500. It works both ways — notation in, decimal out, or the reverse.
Frequently asked questions
What is scientific notation?
It is a compact way to write very large or very small numbers as a coefficient (at least 1 and less than 10) multiplied by a power of ten. For example, 4,500 is 4.5 × 10³ and 0.0031 is 3.1 × 10⁻³.
What is the difference between scientific notation and standard form?
They are the same thing under different names. "Standard form" is the term used in British and many Commonwealth maths syllabuses; "scientific notation" is more common in the United States and in science generally.
What does the "e" mean in a number like 1.5e3?
The e is shorthand for "times ten to the power of", used by calculators and programming languages because they cannot show a superscript. 1.5e3 means 1.5 × 10³ = 1500, and 2.5e-4 means 2.5 × 10⁻⁴ = 0.00025.
What is engineering notation?
Engineering notation is scientific notation with the exponent restricted to multiples of three (…, −6, −3, 0, 3, 6, …). This lines up with the metric prefixes, so 47,000 Ω is written 47 × 10³ Ω — that is, 47 kΩ.
How do I convert a number into scientific notation by hand?
Move the decimal point until exactly one non-zero digit remains to its left. Count the moves: that count is the exponent, positive if you moved left, negative if you moved right. 68,000 → 6.8 with the point moved 4 places left → 6.8 × 10⁴.
How do I turn scientific notation back into an ordinary number?
Shift the decimal point by the exponent — right for a positive exponent, left for a negative one — adding zeros as needed. 3.2 × 10⁵ moves the point five places right to 320,000.
What does a negative exponent mean?
A negative exponent marks a number smaller than one. 10⁻³ is 1/1000 = 0.001, so 5 × 10⁻³ is 0.005. The more negative the exponent, the smaller the number.
Can I enter negative numbers?
Yes. A leading minus sign is kept through every form, so −1500 becomes −1.5 × 10³. The sign belongs to the coefficient, never to the power of ten.
What is the order of magnitude?
It is the exponent of the number in normalised scientific notation — a rough size on a power-of-ten scale. 6.022 × 10²³ has order of magnitude 23. Two numbers with the same order of magnitude are within a factor of ten of each other.
How precise is the conversion?
The tool uses standard double-precision arithmetic, which keeps about 15–16 significant digits. Numbers beyond that range are rounded, as they would be on any calculator; the coefficient shows only the digits that carry meaning.
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