🔬 Scientific Notation Converter
By ToolNimba Math Team · Updated 2026-06-19
Enter a number and press Convert.
Scientific notation writes any number as a digit between 1 and 10 multiplied by a power of ten, which keeps very large and very small values short and readable. This converter goes both ways: type a decimal like 0.00045 or 6500000 to see it in scientific notation, E notation and engineering notation, or paste a value like 4.5 x 10^-4 to expand it back into standard decimal form. It handles negatives, huge numbers and tiny fractions, and lets you round to a chosen number of significant figures.
What is the Scientific Notation Converter?
Scientific notation expresses a number as a x 10^b, where a (the mantissa or coefficient) satisfies 1 <= |a| < 10 and b (the exponent) is a whole number. The exponent simply counts how many places the decimal point moves. A positive exponent means a large number, so 6,500,000 becomes 6.5 x 10^6 because the point shifts six places left. A negative exponent means a small number, so 0.00045 becomes 4.5 x 10^-4 because the point shifts four places right. The sign of the original number is carried on the mantissa, so -0.00045 is -4.5 x 10^-4.
E notation is the same idea written for screens and calculators, where x 10^ is replaced by the letter e (or E). So 6.5 x 10^6 is shown as 6.5e6 or 6.5e+6, and 4.5 x 10^-4 is 4.5e-4. The number after the e is exactly the exponent b. This is the form most spreadsheets, programming languages and scientific calculators use, so being able to read it is handy well beyond a maths class.
Engineering notation is a close cousin of scientific notation, with one extra rule: the exponent is always a multiple of three (..., -6, -3, 0, 3, 6, ...) so the coefficient sits between 1 and 1000. This lines the exponents up with the metric prefixes, where 10^3 is kilo, 10^6 is mega, 10^-3 is milli and 10^-6 is micro. That is why an engineer writes 450 x 10^-6 rather than 4.5 x 10^-4: it reads directly as 450 micro-units. The two notations describe the same value, just grouped differently.
When to use it
- Writing very large quantities like Avogadro's number (6.02214076 x 10^23) or distances in space without a long string of zeros.
- Expressing very small measurements such as the size of an atom or a capacitance in farads in a compact, comparable form.
- Reading or entering numbers in E notation that a calculator, spreadsheet or programming language displayed (for example 6.5e6).
- Converting between scientific and engineering notation so a value lines up with metric prefixes like kilo, mega, milli and micro.
- Rounding a measurement to a fixed number of significant figures for a science or engineering report.
How to use the Scientific Notation Converter
- Pick a direction: "Decimal to notation" to convert a plain number, or "Notation to decimal" to expand a notation value.
- Type your value. For notation you can use forms like 4.5 x 10^-4, 4.5*10^-4 or 6.5e6.
- Optionally choose how many significant figures to round the result to, or leave it as entered.
- Read off the scientific, E and engineering forms (or the expanded decimal), and use the Copy buttons to grab any one.
Formula & method
Worked examples
Convert 6,500,000 to scientific notation.
- Place the decimal point after the first non-zero digit: 6.5
- Count how many places the point moved from its original spot at the end: 6 places left
- Moving left makes the exponent positive, so b = 6
- Write as 6.5 x 10^6 (E notation 6.5e+6)
- Engineering form keeps the same value with a multiple-of-3 exponent: 6.5 x 10^6
Result: 6,500,000 = 6.5 x 10^6 = 6.5e+6
Convert 0.00045 to scientific and engineering notation.
- Place the decimal after the first non-zero digit: 4.5
- The point moved 4 places to the right, so the exponent is negative: b = -4
- Scientific form: 4.5 x 10^-4 (E notation 4.5e-4)
- For engineering form, drop to the nearest multiple-of-3 exponent, -6, and shift the coefficient: 450
- Engineering form: 450 x 10^-6
Result: 0.00045 = 4.5 x 10^-4 = 450 x 10^-6
Expand 3.2 x 10^-3 back to standard decimal form.
- A negative exponent of -3 means move the decimal point 3 places to the left
- Start from 3.2 and shift: 0.32, then 0.032, then 0.0032
- No rounding is needed because the coefficient has only two digits
Result: 3.2 x 10^-3 = 0.0032
How a number maps to scientific, E and engineering notation
| Decimal | Scientific (a x 10^b) | E notation | Engineering |
|---|---|---|---|
| 6,500,000 | 6.5 x 10^6 | 6.5e+6 | 6.5 x 10^6 |
| 12,345 | 1.2345 x 10^4 | 1.2345e+4 | 12.345 x 10^3 |
| 0.1 | 1 x 10^-1 | 1e-1 | 100 x 10^-3 |
| 0.00045 | 4.5 x 10^-4 | 4.5e-4 | 450 x 10^-6 |
| -0.0000005 | -5 x 10^-7 | -5e-7 | -500 x 10^-9 |
Powers of ten and their matching metric prefixes
| Power of 10 | Multiplier | Prefix | Symbol |
|---|---|---|---|
| 10^9 | 1,000,000,000 | giga | G |
| 10^6 | 1,000,000 | mega | M |
| 10^3 | 1,000 | kilo | k |
| 10^-3 | 0.001 | milli | m |
| 10^-6 | 0.000001 | micro | u |
| 10^-9 | 0.000000001 | nano | n |
Common mistakes to avoid
- Getting the sign of the exponent backwards. Moving the decimal point left (for a big number) gives a positive exponent, while moving it right (for a small number) gives a negative one. A common slip is writing 0.00045 as 4.5 x 10^4 instead of 4.5 x 10^-4. If the number is less than 1, the exponent must be negative.
- Leaving the coefficient outside the 1 to 10 range. In proper scientific notation the coefficient must be at least 1 and less than 10, so 65 x 10^5 is not standard form. Shift it to 6.5 x 10^6. Engineering notation is the exception, where the coefficient runs up to (but not including) 1000.
- Confusing engineering notation with scientific notation. They give the same value but group it differently. Engineering notation forces the exponent to a multiple of three, so 4.5 x 10^-4 becomes 450 x 10^-6. Do not expect the coefficient to stay below 10 in engineering form.
- Losing or inventing significant figures when rounding. Rounding 123.456 to three significant figures gives 1.23 x 10^2, not 1.234 x 10^2. Keep exactly the number of meaningful digits you intend, and remember a trailing zero kept on purpose is significant.
Glossary
- Scientific notation
- Writing a number as a x 10^b with the coefficient a between 1 and 10 and an integer exponent b.
- Standard form
- Another name for scientific notation, common in British and international maths teaching.
- Coefficient (mantissa)
- The number a in front of the power of ten, which carries the significant digits and any minus sign.
- Exponent
- The whole number b that tells you how many places, and in which direction, the decimal point moves.
- E notation
- A keyboard-friendly form where x 10^ is replaced by the letter e, so 6.5 x 10^6 is written 6.5e6.
- Engineering notation
- A variant of scientific notation in which the exponent is always a multiple of three, matching metric prefixes.
- Significant figures
- The meaningful digits in a number that carry precision, used when deciding how far to round a result.
Frequently asked questions
What is scientific notation?
Scientific notation writes a number as a coefficient between 1 and 10 multiplied by a power of ten, such as 6.5 x 10^6 for 6,500,000. It keeps very large and very small numbers short and easy to compare. The exponent counts how many places the decimal point moves, positive for big numbers and negative for small ones.
How do I convert a number to scientific notation?
Move the decimal point so that exactly one non-zero digit sits in front of it, then count how many places it moved. If you moved it left the exponent is positive, if you moved it right it is negative. For example 0.00045 becomes 4.5 x 10^-4 because the point moved four places to the right.
What is the difference between scientific and engineering notation?
Both express the same value, but engineering notation forces the exponent to be a multiple of three so the coefficient can run from 1 up to 1000. That lines the exponents up with metric prefixes like kilo, mega, milli and micro. So 4.5 x 10^-4 in scientific notation is 450 x 10^-6 in engineering notation.
What does E notation mean, like 6.5e6?
E notation is scientific notation written for screens and calculators, where x 10^ is replaced by the letter e or E. The number after the e is the exponent, so 6.5e6 means 6.5 x 10^6 and 4.5e-4 means 4.5 x 10^-4. Spreadsheets and programming languages use this form.
How do I convert scientific notation back to a standard number?
Look at the exponent. A positive exponent tells you to move the decimal point that many places to the right (adding zeros if needed), and a negative exponent moves it to the left. For example 3.2 x 10^-3 expands to 0.0032. This converter does the expansion for you in the Notation to decimal mode.
How does this converter handle negative numbers and significant figures?
A minus sign stays with the coefficient, so -0.00045 becomes -4.5 x 10^-4. You can also choose how many significant figures to round to: picking 3 figures turns 123.456 into 1.23 x 10^2. Leave the setting on "Keep as entered" to preserve every digit you typed.