Scientific Notation Converter
Convert between standard decimal numbers, scientific notation, engineering notation and E-notation, or do arithmetic directly on two numbers in scientific notation.
How to use this calculator
- 1Choose whether you want to convert a single number or do arithmetic on two numbers already in scientific notation.
- 2To convert: type a plain decimal, or a number already in E-notation such as 6.022e23. Set significant figures to round, or leave it at zero for full precision.
- 3To calculate: enter each coefficient and exponent, pick an operator (square and square root only need X), and read the result in scientific notation.
How the calculation works
a × 10ⁿ where 1 ≤ |a| < 10- a
- The coefficient — exactly one non-zero digit before the point
- n
- The exponent — how many places the point moves
A positive exponent moves the decimal point right, a negative one moves it left.
Engineering notation restricts the exponent to multiples of three so it maps onto SI prefixes directly.
E-notation (6.022e23) is the same value written for keyboards; it is what calculators and programming languages use.
In arithmetic mode, both numbers are expanded to plain values, the operation is applied, and the result is renormalised so exactly one non-zero digit sits before the decimal point again.
Worked example
Converting 0.00000123
- 1.Move the decimal point right until exactly one non-zero digit sits before it: 1.23.
- 2.That took six places, and moving right means a negative exponent.
- 3.So 0.00000123 = 1.23 × 10⁻⁶.
- 4.In engineering notation the exponent is already a multiple of three, so it is also 1.23 × 10⁻⁶ — the micro prefix.
Result: 1.23 × 10⁻⁶
(6.022 × 10²³) ÷ (2 × 10²³)
- 1.Expand both: 6.022 × 10²³ ÷ (2 × 10²³) is the same as (6.022 ÷ 2) since the powers of ten cancel.
- 2.6.022 ÷ 2 = 3.011.
- 3.The result is already between 1 and 10, so the exponent is 0: 3.011 × 10⁰.
Result: 3.0110 × 10⁰
What scientific notation solves
Scientific notation exists to make extremely large and extremely small numbers manageable, by separating a number into a single meaningful digit (with any decimals) and a power of ten that tracks its scale. Instead of writing out 602,200,000,000,000,000,000,000 with two dozen digits to keep track of, scientific notation writes it as 6.022 × 10²³ — the same value, but with the actual scale of the number visible at a glance instead of buried in a long string of zeros.
Fields that could not function without it
Anywhere a field routinely works with numbers spanning enormous ranges, scientific notation is the default, not an option.
- Astronomy — distances between stars and galaxies, measured in kilometres, would otherwise run to dozens of digits.
- Chemistry — Avogadro’s number (about 6.022 × 10²³) and atomic masses only stay usable written in scientific notation.
- Computing — engineering notation, a close cousin restricted to exponents that are multiples of three, underlies the kilo-, mega- and giga- prefixes used for file sizes and processor speeds.
- Physics — constants like the speed of light and Planck’s constant are always quoted in scientific notation, since their decimal forms would otherwise be dominated by leading or trailing zeros.
Significant figures are the part people get wrong
The digit count in scientific notation is not decoration — it is a claim about precision. Writing a measurement as 1.20 × 10³ instead of 1.2 × 10³ asserts that the trailing zero was actually measured, not just assumed. This is exactly the ambiguity that makes a plain number like 1,200 unclear on its own — does it mean exactly 1,200, or "about 1,200, rounded to two significant figures"? Scientific notation removes the guesswork by making every digit shown a deliberate, counted significant figure.
What this assumes, and where it stops
Assumptions
- The input is a real number within double-precision range.
Limitations
- Limited to about 15–17 significant figures, the precision of double-precision floating point.
- Values beyond roughly 1.8 × 10³⁰⁸ or below 5 × 10⁻³²⁴ cannot be represented.
- Trailing zeros in the input are not preserved as significant, because the numeric value does not record them. Set significant figures explicitly if that matters.
Common questions
What is the difference between scientific and engineering notation?
Scientific notation keeps the coefficient between 1 and 10, so the exponent can be anything. Engineering notation restricts the exponent to multiples of three, so the coefficient can be up to 1000 — but the exponent always corresponds to an SI prefix like kilo, mega or nano, which is far more convenient in engineering work.
How do I count significant figures?
Start at the first non-zero digit and count every digit after it. Leading zeros never count, so 0.00123 has three. Trailing zeros after a decimal point do count, so 1.230 has four. Trailing zeros in a whole number like 1200 are ambiguous, which is exactly why scientific notation is preferred in science.
Can I add or multiply two numbers that are already in scientific notation?
Yes — switch to arithmetic mode and enter each number as a coefficient and exponent. Addition and subtraction first expand both numbers to plain values (their exponents generally differ, so you cannot just add the coefficients); multiplication and division are more direct, since coefficients combine and exponents just add or subtract.
Formula and content last reviewed on .
Results are estimates for information only, not professional advice.
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