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Scientific Notation Calculator (Convert Both Ways, with Steps)

Any number to scientific notation and back, with the decimal-point working, E-notation and engineering notation.

Inputs

Scientific notation
6.022 × 10²³

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What each Scientific Notation input means

Convert
Decimal → scientific writes an ordinary number as m × 10ⁿ; scientific → decimal writes m × 10ⁿ out in full, digit by digit.
Number
The number to convert. Very large or very small values can be typed in E-notation, such as 6.022e23 or 4.7e-13. A number box drops zeros typed at the end of a decimal, so to count significant figures exactly, use the sig fig calculator.
Mantissa
The m in m × 10ⁿ — 6.022 in 6.022 × 10²³. In standard form it is at least 1 and less than 10; other values still work, and the page restates them in standard form.
Exponent
The power of ten, a whole number from −308 to 308: positive for large numbers, negative for small ones.

Scientific Notation formula

x = m × 10ⁿ with 1 ≤ |m| < 10 and n a whole number · n = number of places the decimal point moves (left = positive, right = negative) · engineering notation: n a multiple of 3, 1 ≤ |m| < 1000

x=m×10n,1≤∣m∣<10x = m \times 10^{n}, \quad 1 \le |m| < 10

Scientific notation writes a number as a value between 1 and 10 times a power of ten, so that 2,780,418 becomes 2.780418 × 10⁶ and 0.00000000000047 becomes 4.7 × 10⁻¹³. The exponent is simply how many places the decimal point has to move to leave one non-zero digit in front of it — six places left for the big number, thirteen right for the small one — and the sign of the exponent says which way. Calculators and code write the same thing as 2.780418E6. Engineering notation keeps the exponent a multiple of three so it lines up with kilo, mega, milli and micro: 123,456 is 123.456 × 10³, which reads as 123.456 thousand. The page converts either way and shows the point moving, plus the number of significant figures in what you typed, since scientific notation is the usual way to make that count unambiguous.

Scientific Notation worked example

Avogadro's number, 602,200,000,000,000,000,000,000: the decimal point sits after the last zero and has to move 23 places to the left to leave 6.022, so the number is 6.022 × 10²³, or 6.022E23. Going the other way, 6.022 × 10³ means move the point three places right: 6,022. In engineering notation 6.022 × 10²³ stays as it is, because 23 is not a multiple of 3 — it becomes 602.2 × 10²¹.

More Scientific Notation examples

0.000123: the decimal point moves 4 places right to leave 1.23, so the number is 1.23 × 10⁻⁴, or 1.23E-4. In engineering notation it is 123 × 10⁻⁶ — 123 millionths.

The speed of light, roughly 3 × 10⁸ metres a second, written out: move the decimal point 8 places right to get 300,000,000.

Where the Scientific Notation calculator can give the wrong answer

  • Numbers over about 15 digits lose precision in the box before the page sees them — 602,200,000,000,000,000,000,000 comes through intact only because it has few significant digits; 123,456,789,012,345,678 is not. For long inputs, enter the mantissa and exponent directly.
  • Zero has no scientific notation of the usual kind, since there is no leading non-zero digit; the page shows 0 × 10⁰ by convention.
  • A mantissa outside 1–10 in the reverse direction (60.22 × 10²²) is a valid product but not standard form; the page evaluates it and shows the standard form alongside.
  • Significant figures are counted from the digits you typed, so 6,022 counts 4 and 6,020 counts 3 — trailing zeros in a whole number are treated as placeholders, which is the usual convention but not the only one. Write 6.020 × 10³ if the last zero is measured.
  • The exponent must be a whole number; 10^2.5 is a valid power (316.2) but not scientific notation.

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Scientific Notation FAQ

Move the decimal point until exactly one non-zero digit is to its left, count the places moved, and write the result × 10 to that count — positive if you moved left, negative if right. 37,000 → 3.7 × 10⁴; 0.0052 → 5.2 × 10⁻³. The page shows the move for any number.

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