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Scientific Notation Converter
Convert a number
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Standard decimal—
Scientific notation—
E-notation—
Engineering notation—
Coefficient—
Exponent—
Order of magnitude—
SI prefix—
Significant figures—
Conversion steps
Enter a value to see the decimal-point movement and final equality.
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Scientific notation conversion rules
What scientific notation means
Normalized scientific notation has the form a × 10n, where 1 ≤ |a| < 10 and n is an integer. The sign stays with the coefficient. Zero is handled as a special case.
Decimal to scientific notation
Place the decimal after the first nonzero digit, then count its movement. A move to the left gives a positive exponent; a move to the right gives a negative exponent. Example: 52,000 = 5.2 × 104.
Scientific notation to decimal form
Move the coefficient’s decimal point right for a positive exponent or left for a negative exponent, filling every empty position with a zero. Example: 3.1 × 10−5 = 0.000031.
Normalization and non-normalized input
A coefficient such as 12.3 is accepted, then normalized: 12.3 × 104 = 1.23 × 105. A coefficient of 10 is similarly shifted to 1 while the exponent increases by one.
E-notation
E-notation is a plain-text equivalent: 6.022e23 means 6.022 × 1023. It is convenient in calculators, spreadsheets, and source code.
Engineering notation and SI prefixes
Engineering notation restricts the exponent to a multiple of three and allows a coefficient from 1 to under 1000. Thus 45,000 = 45 × 103, and 103 corresponds to the SI prefix kilo (k).
Significant figures and rounding
Typed decimal zeros are meaningful: 1.2300 retains five significant figures. With “preserve typed precision,” whole-number trailing zeros without a decimal point are treated as placeholders. Custom precision applies exact decimal digit rounding; floor and ceiling respect the sign of negative values.
Scientific notation examples
| Decimal notation | Scientific notation | E-notation | Engineering notation | Exponent direction | Significant figures |
|---|---|---|---|---|---|
| 357096 | 3.57096 × 105 | 3.57096e5 | 357.096 × 103 | Positive; left 5 | 6 |
| 0.005600 | 5.600 × 10−3 | 5.600e-3 | 5.600 × 10−3 | Negative; right 3 | 4 |
| 602200000000000000000000 | 6.022 × 1023 | 6.022e23 | 602.2 × 1021 | Positive; left 23 | 4 |
| −2500 | −2.500 × 103 | -2.500e3 | −2.500 × 103 | Positive; sign unchanged | 4 |
| 0 | 0 × 100 | 0e0 | 0 × 100 | None | 1 |
| 1.2300 | 1.2300 × 100 | 1.2300e0 | 1.2300 × 100 | None | 5 |
Frequently asked questions
What is scientific notation?
Scientific notation writes a number as a × 10^n, where 1 ≤ |a| < 10 and n is an integer. The coefficient a keeps the significant digits and the exponent n records the decimal-point shift.
How do I convert a decimal to scientific notation?
Move the decimal point until one nonzero digit remains to its left. Count the places moved: moving left gives a positive exponent and moving right gives a negative exponent.
How do I convert scientific notation to decimal form?
Move the coefficient’s decimal point by the exponent: right for a positive exponent and left for a negative exponent. Insert zeros wherever the moved decimal point passes an empty place.
Why does a negative exponent create a small decimal?
A negative exponent means a reciprocal power of ten: 10^-n = 1/10^n. Multiplying by it moves the decimal point left, so the absolute value becomes smaller.
How many places should I move the decimal point?
Move it exactly |n| places when converting from a × 10^n. When creating scientific notation, the number of places needed to leave one nonzero digit on the left becomes |n|.
Does zero have scientific notation?
Zero is commonly written as 0 × 10^0 for conversion purposes. Its order of magnitude is undefined because no power of ten gives zero a nonzero leading digit.
How do negative numbers work in scientific notation?
Keep the minus sign on the coefficient and normalize its absolute value, so -4500 becomes -4.5 × 10^3. The exponent describes decimal position, not the sign of the number.
Is 10 × 10^n normalized scientific notation?
No. A normalized coefficient must satisfy 1 ≤ |a| < 10. Rewrite 10 × 10^n as 1 × 10^(n+1).
What does E mean on a calculator?
E means “times ten raised to.” For example, 6.022e23 is the plain-text form of 6.022 × 10^23; it does not mean Euler’s number in this context.
How are significant zeros handled?
Zeros after a decimal and after a nonzero digit are retained as significant, so 1.2300 has five significant figures. Trailing zeros in a whole number without a decimal point are treated as placeholders unless you choose a custom precision.
How is engineering notation different?
Engineering notation uses an exponent divisible by 3 and a coefficient from 1 up to, but not including, 1000. This aligns powers of ten with SI prefixes such as milli, kilo, and mega.