Scientific Notation Converter
Converts between ordinary numbers and scientific, engineering and E notation.
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Your details
Enter an ordinary number or one already in E notation.
Result
- Scientific notation
- 4.20000000 × 10^-4
- E notation
- 4.20000000e-4
- Engineering notation
- 420.000000 × 10^-6
- Ordinary number
- 0.00042
- Significant figures
- 2
Mantissa kept between 1 and 10
Exponent kept to a multiple of three, matching SI prefixes
As written, before any rounding
Writing 0.00042 in standard form…
x = m × 10ⁿ, where 1 ≤ |m| < 10
Move the point 4 places right, so n is negative
m = 4.20000000, n = -4
0.00042 = 4.20000000 × 10^-4
Formula — written step by step
Writing 0.00042 in standard form…
x = m × 10ⁿ, where 1 ≤ |m| < 10
Move the decimal point right until one non-zero digit sits before it
0.00042 → 4.2, which took 4 places
Moving right makes the exponent negative
0.00042 = 4.2 × 10⁻⁴
m is the mantissa, always at least 1 and less than 10, and n counts the places the point moved. Moving right gives a negative exponent, moving left a positive one.
A worked example
A very large number
- Number
- 299,792,458
- Context
- the speed of light in m/s
- Place the point after the first digit: 2.99792458
- Count the places moved: 8, to the left
- Moving left makes the exponent positive
- Round the mantissa to 3 significant figures
2.998 × 10⁸ m/s
The exponent, 8, tells you the number has nine digits before the decimal point. This is the practical value of standard form: the exponent alone conveys the scale, so two quantities can be compared at a glance without counting zeros.
How to use this calculator
- Enter an ordinary number, or one already in E notation such as 4.2e-4 — both are recognised.
- Read the scientific form, where the mantissa is always between 1 and 10.
- Use the engineering row when you need SI prefixes: its exponent is always a multiple of three, matching kilo, mega, milli and micro.
- The significant-figures row reflects how you wrote the number, which is what determines the precision you are claiming.
Why standard form exists
Scientific notation writes any number as a value between 1 and 10 multiplied by a power of ten. Its purpose is not brevity but clarity: 0.00000000662607 is hard to read and easy to mistype, while 6.62607 × 10⁻⁹ states the scale and the precision separately and unambiguously.
It also makes arithmetic across scales tractable. Multiplying two numbers in standard form means multiplying the mantissas and adding the exponents — two small operations instead of one long and error-prone one.
Scientific, engineering and E notation
Scientific notation keeps the mantissa between 1 and 10. Engineering notation relaxes that, allowing a mantissa up to 1000 so the exponent can stay a multiple of three; 47,000 becomes 47 × 10³ rather than 4.7 × 10⁴, which reads directly as 47 kilo-anything.
E notation is the plain-text form used by calculators, spreadsheets and programming languages, because superscripts are awkward to type. 4.2e-4 means exactly the same as 4.2 × 10⁻⁴. All three describe the identical number and this converter shows them together.
Precision travels with the mantissa
One of the most useful properties of standard form is that it separates magnitude from precision. All the significant figures live in the mantissa; the exponent only positions the decimal point. Writing 1.20 × 10³ claims three significant figures, while 1.2 × 10³ claims two, even though both equal 1200.
Ordinary notation cannot express that distinction. Written as 1200, it is genuinely ambiguous whether the trailing zeros are measured or merely placeholders. This is why scientific work reports results in standard form as a matter of course.
Exponents, prefixes and scale
| Power of ten | Prefix | Symbol | Ordinary form |
|---|---|---|---|
| 10⁹ | giga | G | 1,000,000,000 |
| 10⁶ | mega | M | 1,000,000 |
| 10³ | kilo | k | 1,000 |
| 10⁰ | — | — | 1 |
| 10⁻³ | milli | m | 0.001 |
| 10⁻⁶ | micro | µ | 0.000001 |
| 10⁻⁹ | nano | n | 0.000000001 |
SI prefixes step in powers of a thousand, which is exactly why engineering notation keeps its exponent to multiples of three — every value maps directly onto a named prefix.
Frequently asked questions
What is the difference between scientific and engineering notation?
Scientific notation keeps the mantissa between 1 and 10. Engineering notation allows it up to 1000 so the exponent stays a multiple of three, which lines up with SI prefixes like kilo, mega and milli.
Why is the exponent negative for small numbers?
Because you divide by a power of ten rather than multiplying. 4.2 × 10⁻⁴ means 4.2 divided by 10,000. The negative sign marks division, not a negative value.
How do I type scientific notation?
Use E notation: 4.2e-4 or 4.2E-4. This converter also accepts the × 10^ form written out.
What is the standard form of zero?
Zero has no standard form, because no mantissa between 1 and 10 multiplied by any power of ten gives zero. It is conventionally left as 0.