Scientific Notation Converter
Enter a number — as a plain decimal, in E-notation, or in 1.23 × 10^4 form — and instantly see its scientific, engineering, decimal and E-notation equivalents, along with its order of magnitude and the significant-figure count of the original input string.
Please enter a valid number
Scientific notation
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- Engineering notation
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- E-notation
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- Decimal
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- Order of magnitude (Power of 10 the value sits at.)
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- Input sig figs
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Engineering notation always uses an exponent that is a multiple of three — matching SI prefixes (k, M, μ, n, …).
All outputs are rounded to the chosen significant figures. The detected sig-fig count reads the original string (e.g. "1.20" → 3, "1.2" → 2).
Formula
Scientific: n = m × 10^e where 1 ≤ |m| < 10 Engineering: n = m × 10^e where e is a multiple of 3 and 1 ≤ |m| < 1000 Order of magnitude: order = ⌊log₁₀|n|⌋
- · All output values are rounded to the chosen significant-figure count (default 6; pick from 3, 4, 5, 6, 8, 10).
- · Engineering notation always uses an exponent that is a multiple of 3 — matching SI prefixes: 10³ = k (kilo), 10⁶ = M (mega), 10⁻³ = m (milli), 10⁻⁶ = μ (micro), and so on.
- · The input accepts many forms: 12345.6789, 1.23e4, 1.23E+4, 1.23 × 10^4, 1.23×10^4, 1.23 x 10^4, 2 * 10^3.
- · The "input sig figs" count follows the standard convention (IUPAC; Brown/LeMay/Bursten §1.5): trailing zeros in a plain integer are NOT significant ("1200" → 2, "1200." → 4, "1200.0" → 5, "0.00120" → 3).
- · For zero the order of magnitude is shown as "—" because log₁₀(0) is undefined.
- · Output exponents are written as 10^n so the result can be pasted into LaTeX, plain text or word processors as-is.
Frequently asked
What is the difference between scientific and engineering notation?
Scientific notation constrains the mantissa to 1 ≤ |m| < 10 so order-of-magnitude is easy to read. Engineering notation constrains the exponent to multiples of 3 so it lines up with SI prefixes. For example 12345 is 1.2345 × 10⁴ in scientific form but 12.345 × 10³ (i.e. 12.345 kilo-) in engineering form. Electronics, signal processing and analytical chemistry typically prefer engineering notation.
Why does "1200" count as 2 sig figs but "1200." count as 4?
Trailing zeros in a plain integer are ambiguous — they may be measured or may be placeholders. The standard convention (IUPAC and major chemistry textbooks): without a decimal point, trailing zeros are NOT significant; if you write "1200." or "1.200 × 10³", all zeros are then significant. Scientific notation is the unambiguous way to convey precision.
Can I mix "1.23e4" style and "1.23 × 10^n" style?
Both are accepted, including signs (1.23e-4, 1.23 × 10^-4) and any of ×, x, * for the multiplication symbol. E-notation originates from FORTRAN and ALGOL and is defined by the IEEE 754 floating-point I/O standard, so virtually every programming language, spreadsheet and calculator accepts it. Convention: × 10^n for human-readable text; e-notation for code, CSV files and spreadsheets.
What is "order of magnitude" useful for?
Order of magnitude = ⌊log₁₀|n|⌋ — that is, the exponent in the scientific form. It lets you compare two values by powers of ten at a glance: 10⁸ versus 10³ differs by 5 orders of magnitude. Physics back-of-envelope estimates (Fermi problems), astronomical distances, earthquake magnitudes (energy ≈ ×31.6 per unit) and Big-O complexity discussions all lean on order-of-magnitude reasoning to compress detail.
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