Scientific notation converter
Put 47000 in. Scientific notation gives 4.7 × 10⁴, which is correct and tells you nothing you can say out loud. Engineering notation gives 47 × 10³ and the prefix row says kilo, so the value is 47 k — a resistor value, read off without a second thought. That is the entire reason the two notations both exist.
Enter a number and get it in scientific notation — one non-zero digit before the point — along with e notation, engineering notation and the SI prefix that matches. 0.00045 is 4.5 × 10⁻⁴ scientifically, 4.5e-4 in e notation, and 450 × 10⁻⁶ for engineering, which is 450 micro. You can go the other way too: give a mantissa and an exponent and the decimal row expands it.
How to use it
Scientific notation is a strict format — exactly one non-zero digit before the point — and the strictness is what makes it useful rather than merely compact. Two numbers written that way compare by exponent first and by mantissa only if the exponents tie, so 3.2 × 10⁸ beats 9.9 × 10⁷ at a glance without counting a single zero.
Standard form is the same thing under another name
British and Commonwealth schools teach this as standard form, American ones as scientific notation, and the rule is identical: a mantissa at least 1 and below 10, times a power of ten. If you were taught standard form, everything on this page is the notation you already know. The only place the names diverge is in casual use, where "standard form" occasionally means the ordinary decimal writing instead, so it is worth being explicit about which you mean when it matters.
Engineering notation trades the rule for readability
Engineering notation keeps the exponent to a multiple of three and lets the mantissa run from 1 to just under 1000. That breaks the one-digit rule on purpose, because the SI prefixes are spaced in thousands: kilo, mega, giga going up, milli, micro, nano, pico going down. 47000 is 4.7 × 10⁴ scientifically and 47 × 10³ for engineering, and only the second reads as 47 k. A capacitance of 0.00000022 F is 2.2 × 10⁻⁷ scientifically, which is arithmetically fine and useless on a parts list, and 220 × 10⁻⁹ for engineering, which is 220 nF — the number actually printed on the component. Nothing converts between them, because the conversion is a division by a power of a thousand and the mantissa row tells you what it comes to.
The e has nothing to do with Euler
In 4.5e-4 the e means "times ten to the power of" and is pure typography, invented so that exponents survive a plain-text field. It is not the constant 2.71828, and the collision is unfortunate but universal — every spreadsheet, calculator and programming language uses it. A spreadsheet will switch to it without asking when a column is too narrow or a value exceeds about fifteen digits, which is why an order number or a long identifier occasionally arrives in a CSV as 1.23457e+14 with its last digits permanently gone.
Where the round trip stops being exact
Everything here runs in double-precision floating point, which holds roughly 15 to 17 significant digits. A mantissa longer than that is rounded to the nearest representable value on the way in, so expanding a very long number and converting it back can return something a digit or two different at the tail. That is a property of the storage rather than of the notation, and it is the same limit that makes a spreadsheet quietly ruin a long account number. If the digits matter individually, they are an identifier and not a quantity, and they should be kept as text.
What people use it for
- Writing a measurement in standard form for a physics or chemistry answer
- Turning a component value into the engineering form printed on the part
- Working out which SI prefix a value belongs to
- Expanding a mantissa and exponent back to a plain decimal
- Reading a number a spreadsheet has rewritten as 1.23e+14
- Comparing two very different magnitudes without counting zeros
Questions
Scientific notation keeps exactly one digit before the point. Engineering notation holds the exponent to a multiple of three and lets the mantissa run up to 1000, so it lines up with the SI prefixes. 47000 is 4.7 × 10⁴ scientifically and 47 × 10³ for engineering, which reads as 47 k.
Yes. Standard form is the name used in British and Commonwealth schools for exactly the same format: a mantissa from 1 up to but not including 10, multiplied by a power of ten. Nothing about the arithmetic differs.
"Times ten to the power of". It is notation for plain-text fields and has nothing to do with Euler’s number, despite the letter. So 4.5e-4 is 0.00045, and 1.6e9 is 1,600,000,000.
Because the column was too narrow or the value passed the point where the spreadsheet switches display formats. If it was an account number or a barcode, the trailing digits may already be gone for good, since a double only holds about fifteen to seventeen significant digits. Long identifiers belong in a text column.
Engineering, every time. A value in it converts to picofarads, nanofarads or megohms by inspection, because the exponent is already the prefix. Scientific notation makes you do a second conversion in your head before you can read a part off a reel.
Compare the exponents first and only look at the mantissas if the exponents are equal. That single-digit-before-the-point rule is what buys you this — it guarantees every mantissa sits in the same range, so the exponent alone orders the numbers.
A double holds about 15 to 17 significant digits, so a longer mantissa is rounded to the nearest value it can actually store. The change is in the last digits and is a limit of binary floating point rather than of the notation.