Free scientific notation calculator
Express any number in scientific notation — enter a standard or scientific notation number to convert it instantly, updated live, as you type.
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Result shown as mantissa × 10^exponent form. Uses IEEE 754 double precision.
Results are estimates. Consult a professional.
How the scientific notation calculator works
Scientific notation expresses any number as a coefficient multiplied by a power of ten: a × 10ⁿ. The coefficient a must satisfy 1 ≤ |a| < 10 — exactly one non-zero digit before the decimal point. To convert, move the decimal point until that condition is met and count the moves: each move left increases n by 1; each move right decreases it by 1.
Worked example: 0.000456 and 3,200,000
Convert 0.000456 (a small decimal) and 3,200,000 (a large integer) into scientific notation to show both directions.
Common scientific measurements in scientific notation
Science and engineering use scientific notation to handle measurements that span dozens of orders of magnitude without cumbersome strings of zeros.
| Quantity | Value | Scientific notation |
|---|---|---|
| Speed of light (m/s) | 299,792,458 | ≈ 3.0 × 10⁸ |
| Electron mass (kg) | 0.000000000000000000000000000000911 | 9.109 × 10⁻³¹ |
| Earth's mass (kg) | 5,972,000,000,000,000,000,000,000 | 5.972 × 10²⁴ |
| Avogadro's number (mol⁻¹) | 602,214,076,000,000,000,000,000 | 6.022 × 10²³ |
| Proton mass (kg) | 0.00000000000000000000000000167262 | 1.673 × 10⁻²⁷ |
| Diameter of hydrogen atom (m) | 0.000000000106 | 1.06 × 10⁻¹⁰ |
| Distance Earth–Sun (m) | 149,600,000,000 | 1.496 × 10¹¹ |
| Planck's constant (J·s) | 0.000000000000000000000000000000000663 | 6.626 × 10⁻³⁴ |
Source: NIST CODATA 2018 recommended values of fundamental physical constants.
Tips for working with scientific notation
Scientific notation is required in chemistry, physics, astronomy, and engineering. These habits prevent the most common errors.
- Keep exactly one digit before the decimal — 12.5 × 10³ is not standard form; rewrite as 1.25 × 10⁴ by moving the decimal one place left and increasing the exponent by 1.
- Multiplying in scientific notation — Multiply the coefficients, then add the exponents: (3 × 10⁴) × (2 × 10³) = 6 × 10⁷. Adjust if the coefficient exceeds 10.
- Dividing in scientific notation — Divide the coefficients, subtract the exponents: (8 × 10⁶) ÷ (4 × 10²) = 2 × 10⁴.
- Adding/subtracting requires matching exponents — Convert both numbers to the same power of ten before adding or subtracting the coefficients.
- Significant figures travel with the coefficient — 3.20 × 10⁵ has three significant figures; 3.2 × 10⁵ has two. The exponent does not affect significant-figure count.
Accuracy and limitations
The conversion between standard decimal and scientific notation is exact — it is purely a change of representation, not a calculation. The number of significant figures displayed is determined by how many digits you enter: trailing zeros in the coefficient are significant. For calculations that chain multiple scientific-notation values, rounding errors accumulate in the least-significant digits of the coefficient; retain extra digits in intermediate steps.
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About this calculator
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