How to convert a number to scientific notation
Move the decimal point until exactly one non-zero digit remains before it The exponent is however many places you moved it (negative if you moved it right) Take 0.0005 as an example. The decimal point needs to move 4 places to the right to land right after the first non-zero digit (the 5), giving a mantissa of 5. Moving right means a negative exponent, so 0.0005 becomes 5 × 10⁻⁴. For a large number like 150, the point moves 2 places to the left to land after the 1, giving 1.5 × 10² — moving left means a positive exponent.
The rule that makes this unambiguous: the mantissa (the number in front of ×10) must always be at least 1 and less than 10. That's what separates "5 × 10⁻⁴" — correct scientific notation — from something like "0.5 × 10⁻³", which is mathematically equal but isn't in proper scientific notation form.
Notation equivalents
| Standard Form | Scientific Notation |
|---|---|
| 0.0005 | 5 × 10⁻⁴ |
| 0.000025 | 2.5 × 10⁻⁵ |
| 0.5 | 5 × 10⁻¹ |
| 3 | 3 × 10⁰ |
| 150 | 1.5 × 10² |
| 4,500 | 4.5 × 10³ |
| 93,000,000 | 9.3 × 10⁵ |
| 602,200,000,000,000,000,000,000 | 6.022 × 10²³ |
Engineering notation
Engineering notation is a close cousin of scientific notation, with the magnitude of the mantissa at least 1 and less than 1000. The exponent is always a multiple of 3, which lines it up directly with SI unit prefixes — 10³ is kilo, 10⁻³ is milli, 10⁶ is nano, 10⁼ is micro — making it especially natural in engineering and physics contexts where these prefixes are already in use. 15,000 is 1.5 × 10⁴ in scientific notation, but 15 × 10³ in engineering notation — both are correct and equal, but follow different conventions.
| Standard Form | Engineering Notation |
|---|---|
| 0.0005 | 500 × 10⁻⁵ |
| 0.000025 | 25 × 10⁻⁶ |
| 0.5 | 500 × 10⁻³ |
| 3 | 3 × 10⁰ |
| 150 | 150 × 10⁰ |
| 4,500 | 4.5 × 10³ |
| 93,000,000 | 93 × 10⁶ |
| 602,200,000,000,000,000,000,000 | 602.2 × 10²¹ |
Choosing the mantissa when you write it
For any nonzero number, there is only one normalized choice per notation: shift the decimal point until the mantissa sits in the required range, then set the exponent to the number of places you moved it. Moving the decimal point left increases the exponent; moving it right decreases the exponent.
For the full rules for both notations — the permitted mantissa ranges, the forms that look valid but are not, and how zero and negative values behave — see the standard form converter.
Looking to go the other direction?
To expand scientific notation back into standard form, use Scientific & Engineering Notation to Standard Form.
Frequently asked questions
What is 0.0005 in scientific notation?
5 × 10⁻⁴ (or 5e-4). The decimal point moves 4 places right to land after the first non-zero digit, giving a negative exponent of -4.
How do I convert a number to scientific notation?
Move the decimal point until exactly one non-zero digit remains before it. The exponent equals how many places you moved it — positive if you moved left (for numbers 10 or greater), negative if you moved right (for numbers less than 1).
Why must the mantissa be between 1 and 10?
That constraint is what makes scientific notation unambiguous — without it, the same number could be written many different ways (0.5 × 10⁻³ and 5 × 10⁻⁴ are mathematically equal, but only the second follows the standard convention).
Does this converter lose precision on very large numbers?
No. Most calculators convert your number through a standard JavaScript number first, which can only represent whole numbers exactly up to 9,007,199,254,740,991 (2&sup53; − 1) — anything larger silently rounds, so 9007199254740993 would quietly become 9007199254740992 before conversion even happens. This converter parses your input as text and works with its digits directly, never converting through that limited number type, so it preserves every digit exactly regardless of how large or how many decimal places your number has.
What is engineering notation, and how is it different from scientific notation?
Engineering notation is scientific notation with the exponent restricted to a multiple of 3, matching SI unit prefixes like kilo (10³) and milli (10⁻³). 15,000 is 1.5 × 10⁴ in scientific notation, but 15 × 10³ (or 15e+3) in engineering notation — the mantissa is allowed to range up to just under 1,000 to make that possible.