How to use
- Choose Convert a number or Calculate.
- To convert, type the number in any form: 45600, 0.0052, 3.7e4 or 3.7 × 10^4.
- Optionally pick a number of significant figures to round to.
- To calculate, enter two numbers and choose ×, ÷, + or −. The answer is rounded by the significant-figure rules, with the steps shown.
How scientific notation works
A number in scientific notation is written as a × 10ⁿ, where 1 ≤ |a| < 10 and n is a whole number.
- Move the decimal point until one non-zero digit is left of it.
- The number of places moved is the exponent: positive for big numbers, negative for numbers below 1.
- E notation is the calculator and spreadsheet form: 3.7E4 means 3.7 × 10⁴.
- Engineering notation keeps the exponent a multiple of 3, so it lines up with SI prefixes such as kilo, micro and pico.
In the UK this is called standard form. In the US, “standard form” usually means the ordinary number.
Examples
- 37,000: move the point 4 places left to get 3.7 × 10⁴.
- 0.0052: move the point 3 places right to get 5.2 × 10⁻³.
- (4 × 10⁵) × (2 × 10⁻⁷): multiply 4 × 2 = 8 and add the exponents 5 + (−7) = −2, giving 8 × 10⁻².
- 5.00 × 10⁻⁵ + 3.00 × 10⁻³: rewrite as 0.0500 × 10⁻³ + 3.00 × 10⁻³ = 3.05 × 10⁻³.
Four ways to write a number
| Number | Scientific | E notation | Engineering |
|---|---|---|---|
| 390,000 | 3.9 × 10⁵ | 3.9E5 | 390 × 10³ (kilo) |
| 1,230,000,000 | 1.23 × 10⁹ | 1.23E9 | 1.23 × 10⁹ (giga) |
| 0.0000741 | 7.41 × 10⁻⁵ | 7.41E-5 | 74.1 × 10⁻⁶ (micro) |
| 0.00000000036 | 3.6 × 10⁻¹⁰ | 3.6E-10 | 360 × 10⁻¹² (pico) |
Significant figures and trailing zeros
Every digit in the front number is significant, so 1.30 × 10³ has three significant figures. Written as 1,300, the trailing zeros are ambiguous, so the calculator treats them as placeholders unless you choose a number of significant figures.
When multiplying or dividing, the answer keeps the fewest significant figures of the inputs. When adding or subtracting, it keeps the fewest decimal places. Rounding here is half up on the exact digits, so 9.995 to 3 significant figures is 1.00 × 10¹.
For powers that aren’t 10, such as 2⁶⁴, use the exponent calculator.