Scientific Notation Calculator
Convert a number to scientific notation, read one back to a plain decimal, or multiply and divide two of them. You also get E notation, engineering notation, and the matching SI prefix.
What the notation means
Scientific notation writes a number as a × 10ⁿ, where the coefficient *a* is at least 1 and less than 10.
The exponent counts how far the decimal point moved. 456,000 becomes 4.56 × 10⁵ — five places left, so a positive five. 0.00000456 becomes 4.56 × 10⁻⁶ — six places right, so a negative six.
A common slip is writing 45.6 × 10⁴. That equals the right value but is not scientific notation, because the coefficient must be under 10. Calculators and graders both care.
Three notations for the same number
Scientific — 4.56 × 10⁻⁶. What you write by hand and in physics or chemistry work.
E notation — 4.56e-6. What calculators, spreadsheets, and programming languages display, because superscripts do not exist in a plain text field. Excel showing 4.56E-06 means exactly the same thing.
Engineering — 4.56 × 10⁻⁶ here, but 45.6 × 10⁻⁹ would be wrong; engineering notation forces the exponent to a multiple of three so it lines up with SI prefixes. That is why electronics uses it: 10⁻⁶ is micro, 10⁻³ is milli, 10³ is kilo. A resistor is 4.7 kΩ, never 4.7 × 10³ Ω.
Multiplying and dividing
The rules are simpler than they look, because the coefficients and the powers are handled separately.
Multiply — multiply the coefficients, add the exponents. (3 × 10⁴)(2 × 10⁵) = 6 × 10⁹.
Divide — divide the coefficients, subtract the exponents. (6 × 10⁹) ÷ (2 × 10⁵) = 3 × 10⁴.
If the resulting coefficient falls outside 1–10, shift it and adjust the exponent to match. (5 × 10³)(4 × 10²) = 20 × 10⁵, which normalises to 2 × 10⁶. This calculator does that step for you.
Addition and subtraction are the awkward ones and are not included here, because both numbers must first be rewritten to the same exponent.
Significant figures
The coefficient carries the significant figures; the power of ten never does. 4.56 × 10⁻⁶ has three, and so does 4.56 × 10²⁰.
This is precisely why scientific notation exists in measurement work. Writing 4,560,000 leaves it genuinely ambiguous whether those trailing zeros were measured or are just placeholders. Writing 4.56 × 10⁶ says three digits were measured, and 4.5600 × 10⁶ says five were.
Frequently asked questions
How do you write a number in scientific notation?
Move the decimal point until exactly one non-zero digit sits in front of it, then count the places you moved. Moving left gives a positive exponent, moving right gives a negative one. 456,000 becomes 4.56 × 10⁵ and 0.00000456 becomes 4.56 × 10⁻⁶.
What does E mean on a calculator?
It is E notation, a plain-text way of writing "times ten to the power of". 4.56e-6 is identical to 4.56 × 10⁻⁶. Calculators, spreadsheets, and programming languages use it because superscript characters are not available in ordinary numeric fields.
What is the difference between scientific and engineering notation?
Engineering notation restricts the exponent to multiples of three so it lines up with SI prefixes such as kilo, milli, and micro. This allows a coefficient between 1 and 1000. It is standard in electronics, where 4.7 kΩ is far more readable than 4.7 × 10³ Ω.
How do you multiply numbers in scientific notation?
Multiply the coefficients and add the exponents. (3 × 10⁴)(2 × 10⁵) = 6 × 10⁹. If the new coefficient lands outside the 1 to 10 range, shift the decimal and adjust the exponent to compensate.
Do trailing zeros in the exponent count as significant figures?
No. Only the coefficient carries significant figures — the power of ten never does. That is the point of the notation: 4.56 × 10⁶ clearly shows three measured digits, while writing 4,560,000 leaves it ambiguous whether the zeros were measured or are placeholders.