Scientific Notation Converter
The notation that makes it possible to write the mass of an electron and the distance to the sun on the same line.
The rules
A number is in scientific notation when it is written as a coefficient multiplied by a power of ten, where the coefficient is at least 1 and less than 10.
To convert a decimal, move the decimal point until exactly one non-zero digit sits to its left, and count the moves. Moving left gives a positive exponent; moving right gives a negative one.
- 0.00045 → move the point 4 places right → 4.5 × 10⁻⁴
- 384,400 → move the point 5 places left → 3.844 × 10⁵
The sign of the exponent tells you the size at a glance: positive means large, negative means small. The exponent is not the number of zeros, it is the number of places the point moved — a distinction that trips people up with numbers like 1.05 × 10⁴.
Engineering notation and SI prefixes
Engineering notation is a variant that restricts the exponent to multiples of three, so it maps directly onto the SI prefixes used in the real world:
| Power | Prefix | Symbol |
|---|---|---|
| 10⁹ | giga | G |
| 10⁶ | mega | M |
| 10³ | kilo | k |
| 10⁻³ | milli | m |
| 10⁻⁶ | micro | µ |
| 10⁻⁹ | nano | n |
| 10⁻¹² | pico | p |
47,000 ohms is 4.7 × 10⁴ in scientific notation but 47 × 10³ in engineering notation — which is simply 47 kΩ, the way it is actually written on a component. This is why engineers prefer it.
Significant figures
Scientific notation makes precision explicit, which ordinary decimal writing cannot. The number 4,500 is ambiguous: it might be precise to two, three or four significant figures. Written as 4.5 × 10³ it is unambiguously two; as 4.500 × 10³, four.
Two arithmetic rules follow. When multiplying or dividing, the answer carries as many significant figures as the least precise input. When adding or subtracting, the answer carries as many decimal places as the least precise input. Reporting more digits than your measurements support is false precision, and it is one of the most common errors in scientific writing.
Frequently asked questions
What is the difference between scientific and standard form?
None — they are the same thing under different names. 'Standard form' is the usual term in British education, 'scientific notation' in American. Both require a coefficient between 1 and 10.
Why do calculators show E notation?
Because superscripts are awkward on a seven-segment display and in plain text. 4.5E-4 means 4.5 × 10⁻⁴. It is the same value written for a keyboard rather than for print, and most programming languages accept it as literal syntax.
How do I multiply numbers in scientific notation?
Multiply the coefficients and add the exponents: (3 × 10⁴) × (2 × 10⁵) = 6 × 10⁹. For division, divide the coefficients and subtract the exponents. If the resulting coefficient falls outside 1 to 10, shift the point and adjust the exponent to match.