Scientific Notation Converter
Convert between standard and scientific notation showing mantissa and exponent separately for very large and small numbers
Scientific Notation
1.25 × 10^4
Standard Notation
12500
Mantissa (a)
1.2500000000
where 1 ≤ a < 10
Exponent (n)
4
power of 10
Formula
Standard = Mantissa × 10^Exponent
12500 = 1.25 × 10^4
How Scientific Notation Works
Scientific notation expresses numbers as a × 10^n, where 1 ≤ a < 10 and n is an integer. So 1,234 = 1.234 × 10^3. 0.000567 = 5.67 × 10^-4. Useful for very large numbers (avogadro's number = 6.022 × 10^23) or very small (the mass of an electron = 9.109 × 10^-31 kg).
Engineering and science use this constantly. Large quantities (atoms, distances in space, file sizes) and tiny quantities (chemical concentrations, microscopic measurements) compress to readable values. A scientific calculator typically displays in scientific notation when results exceed normal precision (usually past 10^9 or below 10^-9).
Scientific Notation Examples
| Number | Scientific Notation |
|---|---|
| 1,000 | 1 × 10^3 |
| 1,500,000 | 1.5 × 10^6 |
| 1,000,000,000 | 1 × 10^9 |
| 0.001 | 1 × 10^-3 |
| 0.0000567 | 5.67 × 10^-5 |
| 6,022 × 10^23 (Avogadro) | 6.022 × 10^23 |
| Speed of light (m/s) | 3 × 10^8 |
| Mass of Earth (kg) | 5.972 × 10^24 |
Frequently Asked Questions
How do I convert by hand?
Move decimal point until you have one non-zero digit before it. Count moves: positive exponent if you moved left (large numbers), negative if you moved right (small numbers). 4567 → 4.567 × 10^3. 0.0023 → 2.3 × 10^-3.
What's 'engineering notation'?
Like scientific notation but exponent must be a multiple of 3 (3, 6, 9, etc.). So 4,567 in engineering notation = 4.567 × 10^3, but 12,345 = 12.345 × 10^3 (not 1.2345 × 10^4). Aligns with SI prefixes: kilo (10^3), mega (10^6), giga (10^9). Engineers prefer this for readability with units.