Scientific Notation Calculator
Convert a decimal number into scientific notation: coefficient × 10^exponent.
Quick answer
- Scientific notation keeps the coefficient between 1 and 10; E-notation is the same value typed for calculators and code (4.2E5 = 4.2 × 10^5).
- Engineering notation forces the exponent to a multiple of 3 so it matches SI prefixes (kilo, mega, milli, micro), with the mantissa between 1 and 1,000.
- The exponent alone tells you the order of magnitude — compare exponents first, coefficients second.
- Worked example — Scientific notation: 4.2 × 10^5 (full example below).
Scientific Notation Calculator
| Scientific notation | 4.2 × 10^5 |
| Coefficient | 4.200000 |
| Exponent | 5 |
| E-notation | 4.2E5 |
| Engineering notation | 420 × 10^3 |
420,000 = 4.2 × 10^5: move the decimal point 5 places left to get a coefficient of 4.2, and those 5 moves become the exponent.
Scientific notation writes very large and very small numbers compactly as a coefficient between 1 and 10 multiplied by a power of ten: 420,000 becomes 4.2 × 10^5, and 0.00056 becomes 5.6 × 10^−4.
Enter any decimal number. The calculator splits it into its coefficient (also called the mantissa), its exponent, and the full written form, so you can copy it into homework, lab reports or code.
The formula
Worked example
420,000 = 4.2 × 10^5: move the decimal point 5 places left to get a coefficient of 4.2, and those 5 moves become the exponent.
The example is pre-loaded in the result panel — press Calculate with your own numbers to replace it.
Notation equivalents
| Standard form | Scientific notation | E-notation | Engineering notation |
|---|---|---|---|
| 42,000,000 | 4.2 × 10^7 | 4.2E7 | 42 × 10^6 |
| 0.00042 | 4.2 × 10^-4 | 4.2E-4 | 420 × 10^-6 |
Every row is the same number written four ways; each cell was produced by this calculator's own formula for that input.
Frequently asked questions
How do I convert back from scientific notation?
Move the decimal point in the coefficient by the exponent: right for a positive exponent, left for a negative one. 5.6 × 10^−4 means moving 4 places left: 0.00056.
Is 42 × 10^4 valid scientific notation?
It equals the right number, but by convention the coefficient must be at least 1 and less than 10, so the standard form is 4.2 × 10^5. Following the convention lets you compare magnitudes at a glance from the exponent alone.
Where is scientific notation used?
Anywhere numbers span huge ranges: distances in astronomy (the Sun is about 1.5 × 10^8 km away), masses of particles, and computer floating-point formats, which are essentially binary scientific notation.
What is the difference between E-notation and engineering notation?
E-notation is the calculator/computer spelling of scientific notation — 4.2E5 means 4.2 × 10^5. Engineering notation keeps the same idea but forces the exponent to a multiple of 3 (…, −6, −3, 0, 3, 6, …) so it lines up with SI prefixes like kilo (10^3) and milli (10^−3); the mantissa then sits between 1 and 1,000 instead of 1 and 10, so 420,000 is written 420 × 10^3.
Category: Math calculators
Sources & methodology
The exponent is floor(log₁₀|x|) and the coefficient is x ÷ 10^exponent, giving 1 ≤ |coefficient| < 10. Engineering notation rounds the exponent down to the nearest multiple of 3 and rescales the mantissa into [1, 1000). E-notation prints the scientific form as coefficient + "E" + exponent.
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