Scientific notation (standard form) writes any number as a × 10ⁿ, with a single non-zero digit before the decimal point. It tames numbers that are awkwardly large or small — Avogadro's number is 6.022 × 10²³ rather than a 24-digit string. The exponent n is simply how many places the decimal point moved: left for positive, right for negative. The same value can be written in E-notation (1.23e+6) for calculators and code, or engineering notation (exponents in multiples of three) to line up with SI prefixes.
Reviewed: June 20, 2026 · Author: Naveen P N, Founder — AI Calculator · Verified against: the definition of scientific & engineering notation.
The scientific notation rules
To convert, slide the decimal point until exactly one non-zero digit sits to its left, and count the moves to get the exponent. A large number like 1,230,000 needs the point moved six places left, giving +6; a small number like 0.00045 needs it moved four places right, giving −4. E-notation just swaps "× 10ⁿ" for "eⁿ". Engineering notation regroups the exponent to the nearest lower multiple of three, shifting digits into the coefficient so it maps onto kilo, mega, milli and micro.
Worked example — large and small
Large: convert 1,230,000.
Small: convert 0.00045.
So 1,230,000 is 1.23 × 10⁶ with order of magnitude 6, and in engineering notation it stays 1.23 × 10⁶ (1.23 mega). The small number 0.00045 is 4.5 × 10⁻⁴, order −4, but in engineering notation it becomes 450 × 10⁻⁶ — i.e. 450 micro-units, because −6 is the nearest multiple of three. Tiny values like 0.0000005 collapse neatly to 5 × 10⁻⁷. The coefficient also makes significant figures explicit: 4.5 × 10⁻⁴ clearly carries two significant digits.
Frequently Asked Questions
a × 10ⁿ with 1 ≤ |a| < 10. 1,230,000 = 1.23 × 10⁶; 0.00045 = 4.5 × 10⁻⁴.
Move the decimal to one non-zero digit; count moves. Left = +, right = − exponent.
Scientific notation with "e": 1.23 × 10⁶ = 1.23e+6. Used by calculators and code.
Exponents in multiples of 3 to match SI prefixes. 0.00045 = 450 × 10⁻⁶ (450 micro).
The exponent n. 1.23 × 10⁶ → 6. A gap of 3 ≈ a thousandfold size difference.