Scientific Notation Calculator — Any Number, Written as a × 10ⁿ
Turn a plain decimal into normalized scientific notation and E-notation — or go the other way and expand a mantissa and exponent back into a full decimal.
Convert
Advanced options — display precision
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The conversion
Where your number sits
A magnitude scale from 10⁻⁹ (a billionth) to 10⁹ (a billion). The marker is your number’s exponent — it redraws from your inputs.
- Normalized form always keeps the mantissa at 1 ≤ |m| < 10 — one digit before the point, never zero, never ten.
- At the defaults, 0.00000456 converts to 4.56 × 10⁻⁶, with the mantissa, exponent, E-notation (4.56e-6) and engineering notation shown alongside.
- The arithmetic section multiplies, divides, adds and subtracts in scientific notation: multiply the mantissas and add the exponents; divide the mantissas and subtract the exponents; add or subtract by matching the exponents first.
Turn a plain decimal into normalized scientific notation and E-notation — or go the other way and expand a mantissa and exponent back into a full decimal. Negatives, zero, and the very large and very small all handled.
Arithmetic in scientific notation
Add, subtract, multiply and divide numbers written as a × 10ⁿ — two to start, or chain up to five, worked strictly left to right. The answer comes back normalized, with the working shown.
Two or more numbers, one chain
Advanced options — display precision
The answer
Keep exploring
Three companion tools for harder math.
How it works
Three steps from long decimal to compact power.
Choose a direction
Decimal to scientific for writing compactly, or scientific to decimal for reading a value in full.
Type the number
Any decimal — huge, tiny, negative, or zero. E-notation like 4.56e-6 is accepted too.
Read both forms
The normalized a × 10ⁿ form, plus the E-notation your calculator and spreadsheets use.
The math behind scientific notation
Scientific notation writes a number as a mantissa times a power of ten: a × 10ⁿ. In normalized form the mantissa always satisfies 1 ≤ |a| < 10, which makes any two numbers instantly comparable by exponent alone. To convert, slide the decimal point until one non-zero digit sits before it; the exponent counts the slides — left for large numbers (positive), right for small ones (negative).
Worked examples:
| Decimal | Scientific notation | E-notation |
|---|---|---|
| 0.00000456 | 4.56×10⁻⁶ | 4.56e-6 |
| 1,230,000 | 1.23×10⁶ | 1.23e6 |
| −987.65 | −9.8765×10² | -9.8765e2 |
| 5 | 5×10⁰ | 5e0 |
| 0 | 0×10⁰ | 0e0 |
Go deeper
Why the mantissa rule exists, and where E-notation hides in everyday tools.
Without a rule, 1,230,000 could be written 123×10⁴, 12.3×10⁵, or 0.123×10⁷ — all correct, none comparable at a glance. Normalizing fixes that:
- Exactly one digit before the point: the mantissa lives in [1, 10), so the exponent carries the size of the number.
- Comparison becomes trivial: bigger exponent means bigger number — 10⁶ beats 10⁵ without reading digits.
- Sign lives on the mantissa: −9.8765×10² is negative because the mantissa is, not the exponent.
- Zero is the exception: it has no non-zero digit to promote, so it is written 0×10⁰.
Calculators, spreadsheets, and code write ×10ⁿ as the letter e followed by the exponent:
- 4.56e-6 means 4.56 × 10⁻⁶ = 0.00000456 — the number after e is the exponent, sign included.
- 1.23e6 means 1.23 × 10⁶ = 1,230,000 — a missing sign means positive.
- Watch the display limit: pocket calculators switch to E-notation automatically when a result has too many digits for the screen.
- Precision caution: computers store these as binary fractions, so a displayed mantissa is rounded to about 12 significant digits here — plenty for homework and lab work. The Precision setting (under Advanced options in either tool) rounds the notation readouts to 2–10 significant figures when you need them to match a textbook or datasheet.
Engineering notation is scientific notation with one extra rule: the exponent must be a multiple of three. The mantissa then runs from 1 to just under 1,000 instead of stopping at 10:
- 1.23×10⁶ stays 1.23×10⁶ — 6 is already a multiple of three.
- 1.23×10⁴ becomes 12.3×10³ — the point slides one extra place so the exponent lands on 3.
- The steps match the SI prefixes: 10³ is kilo, 10⁶ mega, 10⁹ giga, 10⁻³ milli, 10⁻⁶ micro — which is why datasheets and engineers prefer it.
- Shown on every result: the converter above lists the engineering form under E-notation, in both directions.
E notation: what 1.23E+06 means on a calculator
Calculators rarely display scientific notation with a superscript. Instead they use E notation: 1.23E+06 means 1.23 × 106, and 4.5E−06 means 4.5 × 10−6. The E stands for exponent, and the number after it is the power of 10. The most common misreading is to treat E as Euler’s number or as a unit — it is neither. When you type a value into a calculator in E notation, enter the mantissa, press the EE or EXP key (or type E), then enter the exponent; typing the letter E from the alphabet keys on a phone keyboard will usually not work.
Spreadsheet software uses the same convention: typing 1.23E+06 into a cell stores 1,230,000, and formatting a large number in scientific format displays it as 1.23E+06. If a spreadsheet shows a long number as E notation unexpectedly, the value has not changed — only the display format has. Widen the column or change the number format to General to see the full decimal form.
Scientific notation and significant figures: a natural pair
Scientific notation makes precision visible in a way ordinary decimals do not. The number 120,000 is ambiguous: it could carry two significant figures (1.2 × 105) or six (1.20000 × 105). Written in scientific notation, the trailing zeros after the decimal point in the mantissa are significant by definition, so 1.2 × 105 and 1.200 × 105 say different things and mean different measurements. That is why scientists report results in scientific notation when the precision matters: the notation itself carries the claim about how well the value is known.
The rule for converting is mechanical: every digit in the mantissa counts as significant, including zeros after the decimal point. So 4.50 × 10−4 has three significant figures, and 4.5 × 10−4 has two, even though both describe nearly the same quantity. When this page converts your number, it preserves the digits you entered — add a trailing zero to the mantissa if you mean it to count.
Frequently asked questions
Quick answers about scientific notation.
What is scientific notation?
A way of writing any number as a mantissa times a power of ten — a × 10ⁿ. In normalized form the mantissa is always at least 1 and under 10, so 1,230,000 becomes 1.23×10⁶ and 0.00000456 becomes 4.56×10⁻⁶.
How do I convert a decimal to scientific notation?
Move the decimal point until exactly one non-zero digit sits before it; that is your mantissa. The exponent is how many places you moved — positive if you moved left (large number), negative if you moved right (small number).
What does 4.56e-6 mean?
It is E-notation for 4.56 × 10⁻⁶, which equals 0.00000456. The e replaces “×10^” and the number after it is the exponent — calculators and spreadsheets use it because it fits on one line.
How do I convert scientific notation back to a decimal?
Move the mantissa’s decimal point by the exponent: right for a positive exponent, left for a negative one, padding with zeros. 1.23×10⁶ moves the point 6 places right to give 1,230,000. The Scientific → Decimal mode above does it exactly.
Can the mantissa be negative or 10 or more?
Negative, yes — the mantissa carries the sign, so −987.65 is −9.8765×10². But 10 or more is not normalized: 45.6×10⁵ must be rewritten as 4.56×10⁶ by moving the point and raising the exponent.
How do you add or multiply numbers in scientific notation?
To multiply, multiply the mantissas and add the exponents: 1.5×10³ × 2×10⁴ = 3×10⁷. To divide, divide the mantissas and subtract the exponents. To add or subtract, first rewrite both numbers at the same exponent, then add the mantissas and normalize if the result reaches 10. The arithmetic section on this page does all four for you, and it can chain up to five numbers in one calculation, working strictly left to right.
What is 0 in scientific notation?
Zero is the special case: it has no non-zero digit to place before the point, so it is written 0×10⁰ (0e0 in E-notation). Any exponent would give the same value, and 0 is the convention.
What does E mean in 3.2E+07?
E stands for exponent. 3.2E+07 means 3.2 × 10 to the power 7, which is 32,000,000. The number after E is the power of 10; a negative exponent, as in 3.2E−07, means 3.2 × 10 to the power −7, or 0.00000032.
Can the mantissa be 10 or more in scientific notation?
In normalised scientific notation, no: the mantissa is kept between 1 and 10 (not including 10), with the exponent adjusted to compensate. 12.3 × 10^4 is a valid product, but normalised form is 1.23 × 10^5. This page normalises automatically.
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Disclaimer
This calculator is for information and study only. Conversions use standard double-precision arithmetic with mantissas shown to 12 significant digits; for ultra-precise scientific computing, verify critical figures with dedicated software.