Scientific Notation Converter
Tame unwieldy numbers. Convert a plain decimal into scientific notation (and back), and multiply or divide values that are already in scientific form. Essential for chemistry, physics, and anywhere magnitudes span orders of magnitude — from the mass of a proton to the distance to the Sun.
Decimal → Scientific
Scientific → Decimal
Scientific vs Engineering vs E-Notation — Which to Use?
All three express big/small numbers compactly, but they differ in where the exponent lands and who reads them. Picking the wrong one just makes your result harder to trust:
Four ways to write 0.000045 and 320,000,000
| Rule for the exponentBest | Small example | Large example |
|---|
Engineering notation lines the exponent up with metric prefixes (kilo = 10³, milli = 10⁻³, micro = 10⁻⁶), which is why engineers and lab techs prefer it.
How to Convert and Operate Step by Step
- To scientific: shift the decimal until one non-zero digit sits left of it. Places moved right (small number) → negative exponent; left (big number) → positive. 0.000045 → 4.5 × 10⁻⁵.
- To decimal: move the decimal the exponent's worth of places — positive pushes it right, negative pulls it left. 3.2 × 10⁸ → 320,000,000.
- To multiply: multiply mantissas, add exponents, then re-normalize so the mantissa stays in [1, 10). (2×10³)(3×10⁴) = 6×10⁷.
- To divide: divide mantissas, subtract exponents: (a×10ᵐ) ÷ (b×10ⁿ) = (a/b) × 10ᵐ⁻ⁿ.
- Round sensibly. Keep no more digits than your input's precision justifies — a measurement to 3 sig figs shouldn't yield 12.
Worked Example: How Many Atoms in a Gram of Water?
One water molecule has mass ≈ 2.99 × 10⁻²³ g, and Avogadro's number says there are 6.02 × 10²³ molecules per mole (≈18 g). The number of molecules in 1 g is (1 g) ÷ (2.99 × 10⁻²³ g):
Frequently Asked Questions
What is scientific notation?
A mantissa (1–10) times a power of ten. 0.000045 → 4.5×10⁻⁵.
How do I convert a decimal to it?
Shift the decimal to one non-zero digit left; places moved = exponent (negative for small numbers).
How do I multiply in scientific notation?
Multiply mantissas, add exponents: (a×10ᵐ)(b×10ⁿ) = ab×10ᵐ⁺ⁿ.
Why use it instead of writing zeros?
It reveals order of magnitude at a glance and avoids transcription errors across 50+ orders of magnitude.
How do I divide in scientific notation?
Divide mantissas, subtract exponents: (a×10ᵐ)÷(b×10ⁿ) = (a/b)×10ᵐ⁻ⁿ.