Scientific Notation Calculator
Free scientific notation calculator that converts any number to scientific, E notation, engineering, and standard decimal form, with the exponent and mantissa shown.
Updated 2026-06-09 · Free · No sign-up · Runs privately in your browser
Show the steps & how it's built
Powers of ten & SI prefixes reference
| Power | Prefix | Symbol | Decimal |
|---|
What is a scientific notation calculator?
A scientific notation calculator converts any number into a compact form written as a mantissa multiplied by a power of ten. Type a value such as 123456.789 or 0.00042, press Convert, and this tool returns four results at once: standard scientific notation, E notation, engineering notation, and the plain decimal. It is built for the very large and very small numbers that are awkward to read with long strings of zeros.
Scientific notation (also called standard form in the UK) is the universal shorthand of science, engineering and computing. Instead of writing 0.0000000001, you write 1 × 10^-10. This converter does the place-value counting for you and rounds the mantissa to seven significant figures, so the answer is clean and consistent every time.
How does the calculator work?
The tool rewrites your number n in the form n = m × 10^e, where the mantissa m is at least 1 and under 10 (in absolute value), and e is a whole-number exponent.
The exact method the widget uses:
- Exponent:
e = floor(log₁₀|n|)— the base-10 logarithm of the number’s size, rounded down to the nearest integer. This is the number of places the decimal point moves. - Mantissa:
m = n ÷ 10^e— dividing by that power of ten leaves a value with one digit before the decimal point. - Rounding: the mantissa is rounded to seven significant figures for a tidy result.
From this single calculation it produces all four output forms:
- Scientific notation:
m × 10^ewith 1 ≤ |m| under 10. - E notation: the same value written
m e±e, the format used by calculators and code. - Engineering notation: the exponent is shifted to the nearest multiple of 3, and the mantissa adjusted to match, so it lines up with metric prefixes.
- Standard decimal: the ordinary written-out number.
A positive exponent means a number larger than 1; a negative exponent means a number between -1 and 1. Zero is a special case: it has no leading digit, so it is reported as 0 × 10^0.
Examples
Each example below matches the calculator exactly. Type the input into the tool above to reproduce it.
Example 1: a large number, 123456.789
- The decimal moves five places left, so
e = floor(log₁₀(123456.789)) = 5. - Mantissa:
123456.789 ÷ 10^5 = 1.23456789, rounded to seven significant figures = 1.234568. - Scientific: 1.234568 × 10^5
- E notation: 1.234568e+5
- Engineering: 123.4568 × 10^3 (exponent dropped to the nearest multiple of 3, mantissa multiplied by 100)
Example 2: a small number, 0.00042
- The decimal moves four places right, so
e = floor(log₁₀(0.00042)) = -4. - Mantissa:
0.00042 ÷ 10^-4 = 4.2. - Scientific: 4.2 × 10^-4
- E notation: 4.2e-4
- Engineering: 420 × 10^-6 (next lower multiple of 3 is -6)
Example 3: the speed of light, 299792458
e = floor(log₁₀(299792458)) = 8.- Mantissa:
299792458 ÷ 10^8 = 2.99792458, rounded to seven significant figures = 2.997925. - Scientific: 2.997925 × 10^8
- E notation: 2.997925e+8
- Engineering: 299.7925 × 10^6
Example 4: zero
- Zero has no significant leading digit, so by convention the result is 0 × 10^0, with the decimal form simply 0.
Place-value reference table
This table shows how the exponent counts decimal places. A positive exponent shifts the decimal right when you expand the number; a negative exponent shifts it left.
| Standard decimal | Scientific notation | E notation | Exponent (e) |
|---|---|---|---|
| 1,000,000 | 1 × 10^6 | 1e+6 | 6 |
| 45,000 | 4.5 × 10^4 | 4.5e+4 | 4 |
| 123456.789 | 1.234568 × 10^5 | 1.234568e+5 | 5 |
| 1 | 1 × 10^0 | 1e+0 | 0 |
| 0.00042 | 4.2 × 10^-4 | 4.2e-4 | -4 |
| 0.0000000001 | 1 × 10^-10 | 1e-10 | -10 |
The exponent equals the number of places the decimal point shifts to return the mantissa to its original position — left for positive, right for negative.
What is scientific notation used for?
Scientific notation appears anywhere numbers span a huge range of scale:
- Physics and astronomy. The speed of light (2.997925 × 10^8 m/s) and the distance to stars are unreadable in plain digits, so standard form is the default.
- Chemistry. Avogadro’s number and the size of atoms and molecules are written in powers of ten; a hydrogen atom is roughly 5.3 × 10^-11 m across.
- Engineering. Engineering notation, with exponents in multiples of three, maps directly onto SI prefixes such as kilo (10^3), mega (10^6), milli (10^-3) and micro (10^-6).
- Computing. Programming languages and spreadsheets print floating-point values in E notation, such as
4.2e-4, which is exactly what this tool’s E notation field gives you. - Schoolwork. Standard-form questions are a core topic in algebra and GCSE maths, and this converter shows the mantissa and exponent so you can check your own working.
Tips and common mistakes
- The mantissa must be 1 or more and under 10. Writing
12.3 × 10^4is not proper scientific notation; the correct form is1.23 × 10^5. The calculator always normalises for you. - Count the direction carefully. Moving the decimal left gives a positive exponent; moving it right gives a negative one. This is the most common sign error.
- Engineering is not the same as scientific. Engineering notation allows a mantissa up to but under 1000 so the exponent can stay a multiple of three — that is why 123456.789 shows as 123.4568 × 10^3, not 1.234568 × 10^5.
- Negative numbers keep their sign on the mantissa. A value such as -52000 becomes -5.2 × 10^4; the exponent is based on the size only.
- E notation uses a literal letter e, not Euler’s number.
4.2e-4simply means 4.2 × 10^-4.
Limitations and notes
The mantissa is rounded to seven significant figures, so this tool is a converter rather than an exact-arithmetic engine; numbers with more precision than that are shortened. Extremely large or small magnitudes are still subject to the device’s standard floating-point limits, which can introduce tiny rounding artefacts at the edges. The exponent rule e = floor(log₁₀|n|) is undefined for zero, which is why zero is handled separately as 0 × 10^0. Treat the results as a precise, reference-quality approximation, and follow the rounding and significant-figure rules your instructor or specification requires for graded or professional work.
For more number tools, try the percentage calculator, ratio calculator and square root calculator in the full math calculators category.
Frequently asked questions
How do you convert a number to scientific notation?+
Move the decimal point until one non-zero digit remains to its left, then write the number as that mantissa times 10 raised to the number of places you moved — left moves are positive, right moves negative.
How do you write 123456.789 in scientific notation?+
123456.789 = 1.234568 × 10^5, or 1.234568e+5 in E notation, because the decimal moves five places left and the mantissa rounds to seven significant figures.
What is E notation?+
E notation replaces × 10^e with the letter e, so 1.234568 × 10^5 becomes 1.234568e+5; it is the format calculators and programming languages use for very large or small numbers.
What is engineering notation?+
Engineering notation is scientific notation where the exponent is always a multiple of three, so 123456.789 is written 123.4568 × 10^3, aligning with metric prefixes like kilo, mega and milli.
How do you write 0.00042 in scientific notation?+
0.00042 = 4.2 × 10^-4, because the decimal point moves four places to the right, giving a negative exponent of -4 and a mantissa of 4.2.
What is the scientific notation for zero?+
Zero is written 0 × 10^0; it has no leading significant digit, so the mantissa stays 0 and the exponent is defined as 0 by convention.
How many significant figures does this calculator use?+
The mantissa is rounded to seven significant figures, so a number like 299792458 becomes 2.997925 × 10^8 while keeping enough precision for most science and engineering work.