Quick answer: 299,792,458 (the speed of light in m/s) is 2.99792458 × 10⁸: the decimal point moves 8 places left; in E notation that is 2.99792458E+8.
How it's calculated
In scientific notation a number is written as a × 10ⁿ, where the coefficient a is at least 1 and less than 10 and n is a whole number. Count how many places the decimal point moves: left gives a positive n, right gives a negative n, so 0.000045 = 4.5 × 10⁻⁵.
E notation is the same number written for calculators and spreadsheets: 4.5E-5. Engineering notation keeps n a multiple of 3 so it matches SI prefixes such as kilo (10³), mega (10⁶) and micro (10⁻⁶): 299.792458 × 10⁶.
To multiply, multiply the coefficients and add the exponents; to divide, divide the coefficients and subtract the exponents. Then move the decimal point so the coefficient is back between 1 and 10: (5 × 10³) × (4 × 10²) = 20 × 10⁵ = 2 × 10⁶. For powers on their own see the exponent calculator.
Worked examples
- Large number: 299,792,458 = 2.99792458 × 10⁸
- Small number: 0.000045 = 4.5 × 10⁻⁵
- Multiply: (3 × 10⁸) × (2 × 10⁻³) = 6 × 10⁵
SI prefixes and powers of ten
| Prefix | Symbol | Power |
|---|---|---|
| giga | G | 10⁹ |
| mega | M | 10⁶ |
| kilo | k | 10³ |
| milli | m | 10⁻³ |
| micro | µ | 10⁻⁶ |
| nano | n | 10⁻⁹ |
Frequently asked questions
Why must the coefficient be between 1 and 10?
It makes the form unique and easy to compare: the exponent alone tells you the order of magnitude.
What does 1.5E+8 mean?
It is E notation for 1.5 × 10⁸ = 150,000,000. The E stands for "times ten to the power".
How do I add numbers in scientific notation?
Rewrite them with the same exponent first, then add the coefficients: 3 × 10⁴ + 5 × 10³ = 3 × 10⁴ + 0.5 × 10⁴ = 3.5 × 10⁴.
How is the speed of light written in scientific notation?
2.99792458 × 10⁸ m/s. Most people round it to 3 × 10⁸.
How do I write 0.000045?
4.5 × 10⁻⁵. The decimal point moves five places to the right, so the power is −5.
How do I multiply numbers in scientific notation?
Multiply the front numbers and add the powers. (3 × 10⁸) × (2 × 10⁻³) is 6 × 10⁵.