🔬 Scientific Notation Converter
Convert between standard form, scientific notation, E-notation and engineering notation – exactly, even for huge or tiny numbers.
Quick answer: 299,792,458 in scientific notation is 2.99792458 × 10⁸ (E-notation 2.99792458E+8), and in engineering notation it is 299.792458 × 10⁶.
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Scientific Notation Converter inputs
Result
Scientific notation
2.99792458 × 10⁸
| Scientific notation | 2.99792458 × 10⁸ |
| E-notation | 2.99792458E+8 |
| Engineering notation | 299.792458 × 10⁶ |
| Standard form | 299,792,458 |
| Mantissa (coefficient) | 2.99792458 |
| Exponent (power of 10) | 8 |
| SI prefix (engineering) | M (mega) |
| Significant figures | 9 |
Step by step
- Significant digits: 299792458
- Move the decimal point 8 places to the left so one non-zero digit is in front of it
- Mantissa: 2.99792458, which is between 1 and 10
- Exponent: 8 → 2.99792458 × 10⁸
- Engineering notation rounds the exponent down to a multiple of 3: 6 → 299.792458 × 10⁶
Powers of ten and SI prefixes
| Power | Standard form | Prefix | Name |
|---|---|---|---|
| 10¹² | 1,000,000,000,000 | T (tera) | trillion |
| 10⁹ | 1,000,000,000 | G (giga) | billion |
| 10⁶ | 1,000,000 | M (mega) | million |
| 10³ | 1,000 | k (kilo) | thousand |
| 10⁰ | 1 | – | one |
| 10⁻³ | 0.001 | m (milli) | thousandth |
| 10⁻⁶ | 0.000001 | µ (micro) | millionth |
| 10⁻⁹ | 0.000000001 | n (nano) | billionth |
| 10⁻¹² | 0.000000000001 | p (pico) | trillionth |
What scientific notation is
Scientific notation writes any number as a mantissa between 1 and 10 multiplied by a power of ten. It makes very large and very small numbers short, easy to compare and easy to multiply.
N = a × 10ⁿ, where 1 ≤ |a| < 10 and n is an integer
How to convert
- Find the first non-zero digit and put the decimal point right after it.
- Count how many places the point moved. Moving left gives a positive exponent; moving right gives a negative one.
- Drop leading zeros, keep significant trailing zeros.
Example: the speed of light, 299,792,458 m/s. The point moves 8 places left, so it is 2.99792458 × 10⁸ m/s, written 2.99792458E+8 in E-notation. In engineering notation the exponent must be a multiple of 3, so it becomes 299.792458 × 10⁶ m/s – that is, 299.792458 megametres per second.
Examples
| Standard | Scientific | E-notation | Engineering |
|---|---|---|---|
| 45,000 | 4.5 × 10⁴ | 4.5E+4 | 45 × 10³ |
| 0.0032 | 3.2 × 10⁻³ | 3.2E-3 | 3.2 × 10⁻³ |
| 0.000052 | 5.2 × 10⁻⁵ | 5.2E-5 | 52 × 10⁻⁶ |
| 602,200,000,000,000,000,000,000 | 6.022 × 10²³ | 6.022E+23 | 602.2 × 10²¹ |
Calculating with scientific notation
- Multiply: multiply the mantissas and add the exponents – (3 × 10⁴)(2 × 10⁵) = 6 × 10⁹.
- Divide: divide the mantissas and subtract the exponents.
- Add or subtract: rewrite both numbers with the same exponent first.
Trailing zeros in a whole number such as 45,000 are treated as placeholders. To keep them as significant figures, type a decimal point (45000.) or use the significant figures box.
Frequently asked questions
How do I convert a number to scientific notation?
Move the decimal point until exactly one non-zero digit is in front of it. The number of places you moved it is the exponent: positive if you moved left (big numbers), negative if you moved right (small numbers). 45,000 becomes 4.5 × 10⁴ and 0.0032 becomes 3.2 × 10⁻³.
What is E-notation?
E-notation is how calculators and programming languages write scientific notation: the “E” means “times ten to the power of”. 6.02E+23 is 6.02 × 10²³ and 1.5E-7 is 1.5 × 10⁻⁷.
What is the difference between scientific and engineering notation?
Scientific notation keeps the mantissa between 1 and 10. Engineering notation lets it be between 1 and 1,000 so that the exponent is always a multiple of 3, matching SI prefixes such as kilo (10³), mega (10⁶) and micro (10⁻⁶).
Are the digits exact?
Yes. The converter works on the digits as text instead of floating-point numbers, so even a 40-digit number or an exponent of −300 converts without rounding errors.