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
How Scientific Notation Works
A number becomes m × 10ⁿ where 1 ≤ m < 10 and n is an integer:
0.000045 = 4.5 × 10⁻⁵ | 320,000,000 = 3.2 × 10⁸
Moving the decimal right to shrink the number gives a negative exponent; moving it left to grow the number gives a positive one. Multiplying/dividing in this form is just mantissa math plus exponent addition/subtraction: (2×10³)(3×10⁴) = 6×10⁷.
Worked Example: The Size of a Virus vs a Star
A typical virus is about 0.000045 m across → 4.5 × 10⁻⁵ m. The Sun is roughly 1.39 × 10⁹ m in diameter. The ratio is about (1.39×10⁹) ÷ (4.5×10⁻⁵) ≈ 3.1 × 10¹³ — thirty trillion times larger. Scientific notation turns that comparison from an unreadable string of zeros into a single clean exponent.
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.
How do I divide in scientific notation?
Divide mantissas, subtract exponents: (a×10ᵐ)÷(b×10ⁿ) = (a/b)×10ᵐ⁻ⁿ.