Scientific Notation Converter

Why 1500 has three right answers

Write 1500 and you have said nothing about how precisely it was measured. It might be a count of exactly one thousand five hundred things. It might be a length measured to the nearest ten. It might be a crowd estimate good to the nearest few hundred. The written form is identical in all three cases.

Scientific notation cannot be that vague, because the mantissa is the precision claim. So the same number becomes:

These are different statements about reality, and a converter that picks one silently has made a claim on your behalf. Most of them pick the last, because keeping every digit looks like being careful. It is the opposite: it asserts a hundredfold tighter measurement than the input supported.

This page defaults to the fewest significant figures your input could mean, and shows the alternatives beside it. The reasoning is that the two errors are not symmetrical. Under-claiming is recoverable — you know your own measurement and can add the digits back. Over-claiming is not, because once an invented digit is written down, nothing downstream can tell it from a measured one.

To remove the ambiguity at the source, write a decimal point after the number — 1500. is unambiguously four significant figures — or write it in scientific or E-notation in the first place, which is the form that cannot be vague.

Counting significant figures

The rules are short and the exceptions are where people go wrong.

Every non-zero digit counts. Always, wherever it sits.

Zeros between non-zero digits count. 1005 has four; the zeros are doing real work.

Leading zeros never count. 0.00420 has three significant figures, not six. The zeros before the 4 are only locating the decimal point — which you can see immediately in scientific notation, where they vanish into the exponent: 4.20 × 10⁻³.

Trailing zeros after a decimal point count. 4.20 has three, not two. Writing that final zero is a deliberate claim; there would be no other reason to type it.

Trailing zeros in a bare integer are ambiguous, which is the case above and the only genuinely hard one. 1500, 420 and 90000 all have this problem. Nothing in the notation distinguishes a measured zero from a placeholder, and this is the specific gap scientific notation was designed to close.

Engineering notation is a different thing

Scientific notation keeps exactly one digit before the point, so the mantissa runs from 1 up to 10. Engineering notation instead constrains the exponent to a multiple of three, letting the mantissa run from 1 up to 1000.

That single constraint is what makes it useful, because the SI prefixes are themselves powers of a thousand. An engineering exponent always has a prefix waiting for it: 10³ is kilo, 10⁶ is mega, 10⁻⁶ is micro. So 15000 written as 15 × 10³ reads directly as 15 k — 15 kilohms, 15 kilonewtons, 15 kilometres — while the scientific 1.5 × 10⁴ corresponds to no prefix at all and has to be mentally shifted before it can be spoken.

This is why electronics, mechanical engineering and instrumentation use engineering notation almost exclusively, while physics and chemistry use scientific. Neither is more correct; they are optimised for different things. Scientific notation makes orders of magnitude comparable at a glance, which is what you want when you are reasoning about scale. Engineering notation makes numbers speakable and matches the units they will be written with, which is what you want when you are reading a component value off a datasheet.

One footnote that trips up prefix tables: the SI gained four new prefixes in 2022 — ronna and quetta at 10²⁷ and 10³⁰, ronto and quecto at the matching negative powers. They were added largely because data volumes and some geophysical quantities had outgrown yotta. Many charts still stop at yotta and yocto; this one does not.

Where a spreadsheet stops being exact

Scientific notation is often reached for precisely because a number is too big or too small to write out. That is also the range where the usual tools quietly stop being accurate.

Spreadsheets, pocket calculators and most programming languages hold numbers as binary double-precision floats, which carry about 15 to 17 significant decimal digits. Past that they round, and they do it without saying so. Type a seventeen-digit account number into a spreadsheet cell and the last digit may come back different; type a forty-digit integer and you get a rounded approximation displayed in scientific notation, with no warning that thirty digits were discarded.

This page never uses a float. It works on the digit string you typed, so a forty-digit input round-trips with all forty digits intact, and the tool shows you exactly where a double-precision value would have diverged from it. That comparison is computed rather than asserted — enter a long number and you can watch the two answers part company at a specific digit.

Writing it in each context

The same value has several accepted written forms, and which one to use depends entirely on where it is going.

In prose and print, use the multiplication sign and a real superscript: 6.022 × 10²³. The cross is the convention rather than an asterisk or a letter x, and the superscript should be typeset rather than written as ^23.

In a spreadsheet, a calculator or code, use E-notation: 6.022E23 or 6.022e23. The E stands in for “times ten to the” and is what every one of those tools will parse. Beware that a spreadsheet may also display long numbers this way on its own, which is a formatting decision rather than a statement about your data — and, as above, it may have rounded the value before displaying it.

Where the exponent lands on a multiple of three, consider writing the SI prefix instead of the power: 15 kΩ rather than 1.5 × 10⁴ Ω. It is shorter, it is speakable, and it is what a reader in that field expects.

One thing to avoid everywhere: mixing forms within a single table or set of results. Comparing 1.5 × 10⁴ against 22000 against 15 k means doing three different mental conversions to see which is largest, which is exactly the work a consistent notation is supposed to remove.

Related calculators

Other ways of writing the same number:

More in Conversion, or browse all calculators.

Sources and methodology

Nothing here is fetched and there is no data feed. What the sources settle is not the arithmetic, which is trivial, but the conventions: which digits count as significant, what the prefix set contains after the 2022 additions, and how many decimal digits a binary double can actually hold. Those are the points where a converter can be confidently wrong, so each one is cited to the body that decides it.

• The International System of Units (SI Brochure, 9th edition) — number formatting and the SI prefixesBureau International des Poids et Mesures (BIPM) · verified 2026-09-07 · The prefix set and its multiples of a thousand, which is what engineering notation aligns to, and the SI’s own conventions for writing numbers
• Resolution 3 of the 27th CGPM (2022) — the ronna, quetta, ronto and quecto prefixesGeneral Conference on Weights and Measures (CGPM) · verified 2026-09-07 · The four prefixes added in 2022 at 10^27 and 10^30 and their negative counterparts, which many older prefix tables still omit
• NIST Special Publication 811 — significant digits, rounding, and expressing measurement resultsNational Institute of Standards and Technology, US · verified 2026-09-07 · The rules used here for counting significant figures, including that leading zeros never count, that trailing zeros after a decimal point do, and that trailing zeros in a bare integer are ambiguous
• IEEE 754-2019 — Standard for Floating-Point ArithmeticInstitute of Electrical and Electronics Engineers · verified 2026-09-07 · That binary double precision carries roughly 15 to 17 significant decimal digits, which is the limit the float comparison on this page demonstrates