How scientific notation works
Scientific notation writes a number as a coefficient between 1 and 10 multiplied by a power of ten: 45,600 = 4.56 × 10⁴ and 0.000456 = 4.56 × 10⁻⁴. The exponent counts how many places the decimal point moved. Moving it left (for big numbers) gives a positive exponent; moving it right (for small numbers) gives a negative one.
To go back to standard form, reverse the move: a positive exponent moves the decimal point right, a negative exponent moves it left, filling gaps with zeros. 6.022 × 10²³ is 602,200,000,000,000,000,000,000.
E notation and engineering notation
Calculators, spreadsheets and programming languages can't easily show superscripts, so they write the exponent after an E: 6.022E23 means 6.022 × 10²³, and 1.5E-7 means 1.5 × 10⁻⁷. The E has nothing to do with the constant e (2.718…).
Engineering notation is a variant that only uses exponents divisible by 3, so the coefficient is between 1 and 1,000. That lines up with metric prefixes: 45.6 × 10³ meters is 45.6 kilometers, and 456 × 10⁻⁶ seconds is 456 microseconds.
Significant figures
Scientific notation makes significant figures unambiguous. Every digit in the coefficient counts. Leading zeros never count; zeros between nonzero digits always count; trailing zeros after a decimal point count. Trailing zeros in a whole number such as 1300 are ambiguous — they might be measured or might just hold place — so by convention they're treated as not significant. Writing 1.3 × 10³ (two significant figures) or 1.300 × 10³ (four) removes the doubt.
When you round to fewer significant figures, this calculator uses the familiar rule: look at the first digit you're dropping, and round up if it's 5 or more. Some chemistry courses use round-half-to-even instead; the rounding calculator lets you pick.
Scientific notation
x = a × 10ⁿ, with 1 ≤ |a| < 10E notation: aEnEngineering notation: x = b × 10ᵐ, with m a multiple of 3 and 1 ≤ |b| < 1000- a = the coefficient (also called the mantissa or significand)
- n = the exponent: the number of places the decimal point moves (positive for large numbers, negative for numbers below 1)
Worked example: the speed of light, 299,792,458 m/s
- Move the decimal point 8 places to the left to leave one digit in front: 2.99792458.
- It moved left, so the exponent is +8: 2.99792458 × 10⁸ m/s. In E notation: 2.99792458E8.
- To 3 significant figures: keep 2.99, look at the next digit, 7. It's 5 or more, so round up: 3.00 × 10⁸ m/s.
- Engineering notation: 299.792458 × 10⁶ m/s.
Frequently asked questions
How do I write 0.00056 in scientific notation?
Move the decimal point 4 places to the right to get 5.6, so the exponent is −4: 5.6 × 10⁻⁴.
What does 1.5E-7 mean?
It's E notation for 1.5 × 10⁻⁷, which is 0.00000015. Move the decimal point 7 places to the left.
Is 45 × 10³ in scientific notation?
Not proper scientific notation, because the coefficient must be at least 1 and less than 10. It equals 4.5 × 10⁴. It is valid engineering notation, though.
How many significant figures does 0.004560 have?
Four: 4, 5, 6 and the final 0. The leading zeros only place the decimal point, but a trailing zero after the decimal point is significant. In scientific notation it's 4.560 × 10⁻³.
How do I enter scientific notation on a calculator?
Use the EE or EXP key, which means "× 10 to the power". For 6.022 × 10²³, type 6.022, EE, 23. In spreadsheets, type 6.022E23.
Sources
Last reviewed for 2026. How we calculate.