Scientific Notation Converter
Convert any number to scientific, engineering, and E-notation.
Mantissa between 1 and 10, times a power of ten.
| Form | Value |
|---|---|
| Decimal | 0.00042 |
| Scientific | 4.2 × 10⁻⁴ |
| E-notation | 4.2e-4 |
| Engineering | 420 × 10⁻⁶ |
Scientific notation writes a number as a × 10ⁿ, where the mantissa a is between 1 and 10 and n is an integer. Move the decimal point until one non-zero digit remains on its left, then count the moves. So 0.00042 becomes 4.2 × 10⁻⁴ and 5,300,000 becomes 5.3 × 10⁶.
Taming very large and very small numbers
Scientific notation writes a number as a mantissa between 1 and 10 multiplied by a power of ten. So 0.00042 becomes 4.2 × 10⁻⁴ and 5,300,000 becomes 5.3 × 10⁶. It makes orders of magnitude obvious at a glance and keeps arithmetic with extreme values manageable.
a is the mantissa, n is the integer exponent (negative for small numbers)
Worked example: 0.00042
Move the decimal point until exactly one non-zero digit sits to its left, then count how far it moved.
- 1 Move the decimal point. From 0.00042, move right past the zeros to get 4.2 — the mantissa.
- 2 Count the moves. The point moved 4 places to the right.
- 3 Set the sign of the exponent. Moving right for a number below 1 makes the exponent negative: n = −4.
- 4 Write it out. 0.00042 = 4.2 × 10⁻⁴. For a large number like 5,300,000 the point moves left, giving 5.3 × 10⁶.
Engineering notation and SI prefixes
Engineering notation restricts the exponent to multiples of three, which lines up exactly with the metric prefixes (kilo-, milli-, micro-). That is why electronics and engineering favour it — 4.7 × 10⁻³ F is simply 4.7 mF. For a different way to compress numbers, see the number base converter, and reach for the scientific calculator when you need to compute with these values.
SI prefixes ↔ powers of ten
The common metric prefixes and the exponent each one stands for.
| Prefix | Symbol | Power of ten |
|---|---|---|
| giga | G | 10⁹ |
| mega | M | 10⁶ |
| kilo | k | 10³ |
| (none) | — | 10⁰ |
| milli | m | 10⁻³ |
| micro | µ | 10⁻⁶ |
| nano | n | 10⁻⁹ |
| pico | p | 10⁻¹² |
Why the mantissa rule matters
Keeping the mantissa between 1 and 10 makes the form unique, so 4.2 × 10⁻⁴ and 0.42 × 10⁻³ describe the same number but only the first is in standard scientific notation. It also makes the exponent a clean count of orders of magnitude, which is exactly what lets you compare 6.0 × 10²³ atoms to 9.1 × 10⁻³¹ kg at a glance.