How this calculator works
- Step 1Find the first digit0.000123Skip leading zeros to the first non-zero digit.
- Step 2Move the point1.23Place the point after that digit.
- Step 3Count the places1.23 × 10⁻⁴The places moved become the power of ten.
Scientific notation writes a number as a coefficient from 1 to under 10, times a power of ten. Small numbers get negative powers.
The calculator keeps your digits as an exact decimal, so long or tiny numbers never pick up stray digits from floating point.
Worked example: the speed of light to 3 figures
- Form
a × 10ⁿ, with 1 ≤ a < 10
- aCoefficient 3.00
- nPower of ten 8
- Move the point299792458 → 2.997924588 places left
- Round to 3 figures2.99|792458, next digit 73.00
- Answer3.00 × 10 to the 83.00 × 10⁸
The zeros in 3.00 matter: they show the value is known to three figures. Writing just 3 × 10⁸ would claim only one.
Three ways to write it
- Scientific6.02 × 10²³One digit before the point.
- E notation6.02E23How calculators and spreadsheets show it.
- Engineering602 × 10²¹Powers in steps of 3, matching kilo, mega, giga.
Read the result
A positive power means a big number; a negative power means a number between 0 and 1.
Rounding can carry into a new digit: 9.96 to 2 figures becomes 1.0 × 10¹, not 10 × 10⁰. The calculator handles this.
Assumptions and limits
- Exact digitsUp to 60 digits, with no floating-point error.
- Half upTies round away from zero.
- Typed zeros count123400 keeps all six figures: 1.23400 × 10⁵.
- Very long numbersStandard form is not written out past 100 places.
Related precision tools
Scientific notation keeps the significant digits and moves the decimal point.
To round by significant figures alone, use the significant figures calculator. For whole numbers too large to write this way without losing digits, the big number calculator works exactly.
Common mistakes
Mistake: Writing 12.3 × 10³.
Instead: Keep one digit before the point: 1.23 × 10⁴.
Mistake: Giving 0.000123 a positive power.
Instead: Numbers below 1 have negative powers: 10⁻⁴.
Mistake: Dropping significant zeros.
Instead: Write 3.00 × 10⁸ when three figures are known.
Checking the method
Every golden case is re-formatted with Python's Decimal type, using half-up rounding.
An independent script formats each number with Python’s exact decimal arithmetic and builds the engineering form from its digits.
Read how we test our calculators, or browse more maths calculators.