Scientific Notation Calculator

Your inputs

Convert in either direction

Number

Plain decimal, E notation, or a power of ten — 0.0000123, 1.23e-5 and 1.23 × 10^-5 are the same number and all three are accepted. Digits you type are digits this tool keeps.

Unit (optional)

The symbol the measurement is in — F, m, s, Hz, W. It is attached to the SI prefix, so 0.0000123 F comes back as 12.3 µF.

Your inputs are calculated locally and are not stored.

Scientific notation1.23 × 10⁻⁵

0.0000123 carries 3 significant figures, so the mantissa is written with 3 digits. Grouped to the nearest power of a thousand it is 12.3 × 10⁻⁶, or 12.3 µF — the "micro" range.

Significant figures: 3
Exponent: -5
Engineering exponent: -6
SI prefix: micro (µ)
Value with prefix: 12.3 µF

The same number, written four ways
Notation	Written
Plain decimal	0.0000123
Scientific	1.23 × 10⁻⁵
Engineering	12.3 × 10⁻⁶
E notation	1.23e-5

Every digit you typed is treated as significant, including trailing zeros after the decimal point. Nothing is rounded away and nothing is added.
The significant-figure count describes the scientific mantissa. Engineering notation can pad it — 1 × 10⁵ becomes 100 × 10³ — and those padding zeros are placeholders, not precision.
SI prefixes exist only at multiples of three, which is exactly why engineering notation constrains the exponent that way. There is no prefix for 10⁰, and none past 10³⁰ or 10⁻³⁰.

Formula & methodology

One number, three notations, one set of digits

Every form on this page is the same quantity written with the decimal point in a different place and an exponent making up the difference. Nothing is converted; the point is moved and the exponent is adjusted to compensate.

x = m × 10ⁿ • 1 ≤ |m| < 10 • n_eng = 3 × ⌊n ÷ 3⌋

m: The mantissa — the digits, with the point after the first one
n: The exponent — how many places the point moved, and which way
n_eng: The engineering exponent — the nearest multiple of three at or below n, so an SI prefix exists for it

Why the digit count is the answer, not a detail

The number of digits in the mantissa is the number of significant figures, and that is the whole reason the notation was invented. 1.23 × 10⁻⁵ claims three digits of precision. 1.230 × 10⁻⁵ claims four. They are the same value to a computer and different statements about an instrument, so this calculator parses the characters you typed rather than the number they evaluate to — a trailing zero you wrote is a trailing zero it keeps. If you need to count or round the figures in a plain decimal instead, that is what the significant figures calculator is for.

Why the floor, and not simple truncation

The engineering exponent is 3 × ⌊n ÷ 3⌋, rounding down. Truncating towards zero instead would send −5 to −3 rather than −6, and the mantissa would come out below 1 — 0.123 × 10⁻³ rather than 12.3 × 10⁻⁶. Rounding down keeps the mantissa in the 1-to-1000 range engineering notation is defined on, on both sides of zero.

Worked example

0.0000123 farads, three ways

Start with the decimal. Moving the point right until one non-zero digit stands in front of it takes five places: 0.0000123 becomes 1.23, and each place moved right is one power of ten removed, so the exponent is −5. Scientific notation: 1.23 × 10⁻⁵. Three digits in the mantissa, so three significant figures — the leading zeros never counted, because they only hold the point in position.

Now engineering notation. The multiples of three near −5 are −3 and −6, and the rule takes the one below: −6. Going from 10⁻⁵ to 10⁻⁶ is a factor of ten removed from the exponent, so a factor of ten has to go back into the mantissa — the point moves one place right, 1.23 becomes 12.3. That gives 12.3 × 10⁻⁶. And because 10⁻⁶ is the SI prefix micro, the same capacitor is 12.3 µF — the number actually printed on the part.

A second case shows the ambiguity the notation exists to kill. Type 1200 and this calculator answers 1.2 × 10³: two significant figures, because trailing zeros in a bare whole number are read as placeholders. If you measured all four digits, 1200 gives you no way to say so — but 1.200 × 10³ does, and so does the older convention of writing 1200. with a trailing point. Both are accepted above, and they give different answers, which is the correct behaviour.

SI prefixes

Why the prefixes only exist every third power

The SI prefixes run in steps of a thousand: kilo (10³), mega (10⁶), giga (10⁹), tera (10¹²) going up, and milli (10⁻³), micro (10⁻⁶), nano (10⁻⁹), pico (10⁻¹²) going down, out to quetta (10³⁰) and quecto (10⁻³⁰) since the 27th General Conference on Weights and Measures added the last four in 2022.

There are four survivors from an older scheme that are not multiples of three — deca (10¹), hecto (10²), deci (10⁻¹) and centi (10⁻²) — and outside the centimetre they are barely used. That is precisely why engineering notation is defined the way it is: constrain the exponent to a multiple of three and every result has a prefix, a symbol, and a name a technician already says out loud. There is no prefix at 10⁰, because none is needed.

Assumptions

What this calculator assumes

Every digit you type is significant, including trailing zeros after a decimal point. The one exception is the classical one: trailing zeros in a whole number with no decimal point are read as placeholders, and the result says so when that happens.
Nothing is rounded. This tool re-writes the number you gave it; it does not decide how many figures you should have kept.
Commas are stripped before parsing, so 1,200 is read as 1200. A comma means a decimal point in much of the world, which is exactly why the underlying engine refuses to guess and the input is normalised here instead.
Exponents from −300 to 300 and mantissas up to 17 digits are accepted. Both ceilings come from double-precision floating point, which runs out at about 10³⁰⁸ and carries at most 17 significant decimal digits.
Engineering notation can pad the mantissa with zeros — 1 × 10⁵ becomes 100 × 10³ — and those zeros are placeholders, not precision. The significant-figure count always describes the scientific mantissa.

Common questions

Scientific notation FAQ

How do I write a number in scientific notation?

Move the decimal point until exactly one non-zero digit sits in front of it, then count how many places you moved it. That count is the exponent — negative if you moved right, positive if you moved left. For 0.0000123 you move right five places to reach 1.23, so the answer is 1.23 × 10⁻⁵. For 93,000,000 you move left seven places to reach 9.3, so it is 9.3 × 10⁷. The digits never change; only where the point sits and what the exponent says about it.

What is the difference between scientific and engineering notation?

Scientific notation keeps the mantissa between 1 and 10 and lets the exponent be any whole number. Engineering notation forces the exponent to a multiple of three and lets the mantissa run from 1 up to 1000. The reason is the SI prefixes: they are defined only at every third power of ten, so an engineering exponent always has a name — kilo, mega, milli, micro — and a scientific one usually does not. 1.23 × 10⁻⁵ F is arithmetic; 12.3 µF is a part you can order.

How many significant figures does 1200 have?

By the usual convention, two. Trailing zeros in a whole number written without a decimal point are read as placeholders holding the digits in position, not as measured digits — and the writer has no way, in that notation, to say they meant otherwise. That ambiguity is the single strongest argument for scientific notation: 1.2 × 10³, 1.20 × 10³ and 1.200 × 10³ are two, three and four significant figures, and nobody has to guess. Writing 1200. with a trailing decimal point is the older workaround and this calculator honours it.

What does the e in 1.23e-5 mean?

It is shorthand for '× 10 to the power of', introduced because early calculators and programming languages had no superscripts. 1.23e-5, 1.23E-5 and 1.23 × 10⁻⁵ are the same number written three ways, and this calculator accepts all of them. The e has nothing to do with Euler's number; that collision is unfortunate and permanent.

Why does 0.0000123 farads come back as 12.3 µF?

Because 0.0000123 is 1.23 × 10⁻⁵, and the nearest multiple of three below −5 is −6. Regrouping to 10⁻⁶ moves the point one place right, giving 12.3 × 10⁻⁶ — and 10⁻⁶ is the SI prefix micro, symbol µ. So the same quantity is 12.3 µF, which is how the value is printed on the component and listed in the catalogue.

Can the mantissa be negative?

Yes. The sign belongs to the number, not to the notation: −0.0000123 is −1.23 × 10⁻⁵. What the mantissa cannot be is smaller than 1 or 10 or larger in magnitude — 0.123 × 10⁻⁴ is the same value but is not in standard form, and 12.3 × 10⁻⁶ is engineering notation rather than scientific.

Primary sources

Sources and review notes

The arithmetic here is exact and has no data behind it to go stale: moving a decimal point and counting places. What can change is the prefix table, which last grew in November 2022 when quetta, ronna, ronto and quecto were adopted — those four are included above.