What scientific notation is
Scientific notation writes any number as a × 10ⁿ, where the coefficient a has exactly one non-zero digit before the decimal point (1 ≤ |a| < 10) and n is a whole number. It makes very large and very small numbers easy to read, compare and multiply. The speed of light, 299,792,458 m/s, becomes 2.99792458 × 10⁸; the charge of an electron, 0.00000000000000000016 C, becomes 1.6 × 10⁻¹⁹.
How to convert by hand
- Move the decimal point until a single non-zero digit is left in front of it.
- Count how many places you moved it: that is the exponent.
- Moving left (big numbers) gives a positive exponent; moving right (small numbers) gives a negative one.
So 45,600 = 4.56 × 10⁴ and 0.00042 = 4.2 × 10⁻⁴.
Engineering notation
Engineering notation is the same idea with the exponent restricted to multiples of 3, so the coefficient falls between 1 and 1,000. Each step matches an SI prefix:
| Power | Prefix | Example |
|---|---|---|
| 10⁹ | giga (G) | 2.4 GHz |
| 10⁶ | mega (M) | 299.792458 × 10⁶ m/s |
| 10³ | kilo (k) | 4.7 kΩ |
| 10⁻³ | milli (m) | 250 mA |
| 10⁻⁶ | micro (µ) | 22 µF |
| 10⁻⁹ | nano (n) | 650 nm |
Significant figures
Significant figures are the digits that tell you how precise a value is: every non-zero digit, zeros between non-zero digits and trailing zeros after a decimal point. Leading zeros are never significant. 0.00420 has three significant figures; 1,050 has three or four depending on whether the final zero was measured.
Choose the number of significant figures in the calculator and it rounds the number for you. With the default, 299,792,458 rounded to 3 significant figures is 300,000,000, or 3.00 × 10⁸.
Worked example
Enter 299792458 and 3 significant figures:
- Coefficient: 2.99792458, exponent: 8
- Rounded: 300,000,000 (3.00 × 10⁸)
- Engineering notation: 299.792458 × 10⁶
Typing very large or small numbers
Type numbers in E notation, the format calculators and spreadsheets use: 6.02e23 means 6.02 × 10²³ and 1.6e-19 means 1.6 × 10⁻¹⁹. In a result, a rule of thumb for multiplying is to multiply the coefficients and add the exponents: (3 × 10⁴) × (2 × 10⁵) = 6 × 10⁹.