0.0000000000005 in Scientific Notation
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Scientific Notation
5 × 10^-13
Summary
5E-13 in scientific notation is 5 × 10^-13.
Number A
5 × 10^-13
Engineering: 500 × 10^-15
E-Notation
5E@r.A.Exponent
Order of magnitude
What is Scientific Notation?
Scientific notation represents very large or very small numbers in a compact, consistent form: a significand (also called a mantissa or coefficient), multiplied by 10 raised to an integer exponent, written as b × 10ⁿ. By convention, the significand always has exactly one non-zero digit to the left of the decimal point — so 700 becomes 7 × 10², not 70 × 10¹ or 0.7 × 10³.
This calculator converts any number you enter into scientific notation, engineering notation (where the exponent is restricted to multiples of 3, matching SI prefixes like kilo, mega, and micro), and E-notation (the "7E2" style used in spreadsheets and calculators). It can also perform arithmetic directly between two numbers in scientific notation.
Converting To and From Scientific Notation
0.0004212 = 4.212 × 10⁻⁴
−5,000,000,000 = −5 × 10⁹
To convert a standard number to scientific notation, move the decimal point until exactly one non-zero digit remains to its left, and count how many places you moved it — that count becomes the exponent (positive if you moved left, negative if you moved right). To convert back, simply move the decimal point the opposite direction by the exponent's value.
Arithmetic in Scientific Notation
Addition and subtraction require both numbers to share the same power of 10 first — rewrite one number so its exponent matches the other, then add or subtract just the significands.
Multiplication multiplies the significands and adds the exponents: (1.432×10²) × (8×10⁻¹) = (1.432×8)×10^(2−1) = 11.456×10¹, which renormalizes to 1.1456×10².
Division divides the significands and subtracts the exponents: (1.432×10²) ÷ (8×10⁻¹) = (1.432÷8)×10^(2−(−1)) = 0.179×10³, which renormalizes to 1.79×10².
Engineering Notation vs. Scientific Notation
Engineering notation is a variant that restricts the exponent to multiples of 3 (…, −6, −3, 0, 3, 6, 9, …), so the significand ranges from 1 to just under 1000 instead of 1 to just under 10. This aligns naturally with SI unit prefixes — for example, 4.7 × 10⁶ in engineering notation reads directly as "4.7 mega-" units, which is why engineers and electricians favor it over strict scientific notation.
Why Scientific Notation Matters
Beyond convenience, scientific notation makes it easy to compare the scale of very different numbers at a glance — the exponent alone tells you the order of magnitude. It's the standard way scientific and engineering fields express measurements spanning enormous ranges, from the mass of an electron (9.109 × 10⁻³¹ kg) to the distance to the nearest star (4.0 × 10¹³ km), without writing out dozens of zeros.
Example — Your Current Inputs
5E-13 in scientific notation is 5 × 10^-13.
Additional Example — Astronomical Distances
The Sun is about 150,000,000 kilometers from Earth (1.5 × 10⁸ km), while the nearest star system, Alpha Centauri, is about 40,000,000,000,000 kilometers away (4 × 10¹³ km). Dividing these in scientific notation — (4×10¹³) ÷ (1.5×10⁸) — gives (4 ÷ 1.5) × 10^(13−8) ≈ 2.67 × 10⁵, meaning Alpha Centauri is roughly 267,000 times farther from Earth than the Sun is — a comparison that would be far harder to read with all the zeros written out.
About These Parameters
- Number A / Number B
- Enter numbers in either standard decimal form (700, 0.0004212) or scientific/E-notation (7e2, 4.212e-4) — the calculator accepts either and converts as needed.
- Operation
- Choose "Just Convert" to see Number A's scientific and engineering form alone, or pick an arithmetic operation to combine Number A and Number B and see the result renormalized into proper scientific notation.
Frequently Asked Questions
What's the difference between scientific notation and E-notation?
They represent the same value — E-notation is just a plain-text shorthand that replaces "× 10" with the letter E, since superscript exponents aren't always easy to type or display. 7 × 10² and 7E2 mean exactly the same number, 700.
Why does the significand have to be between 1 and 10?
That's the normalized form convention, which makes scientific notation unambiguous — every number has exactly one correct scientific notation representation. Without the rule, 700 could be written as 7×10², 70×10¹, or 0.7×10³, all technically correct but inconsistent, defeating the purpose of a standard notation.
Can scientific notation represent negative numbers?
Yes — the sign applies to the significand, not the exponent. −5,000,000,000 becomes −5 × 10⁹; the exponent describes the magnitude, and the leading minus sign describes the number's sign, exactly as in standard notation.
Why use engineering notation instead of scientific notation?
Because multiples of 3 map directly onto SI unit prefixes (kilo = 10³, mega = 10⁶, milli = 10⁻³, micro = 10⁻⁶, and so on), engineering notation lets you read off the appropriate unit prefix immediately, which is especially useful in electronics, physics, and other applied sciences.