Scientific Notation
Scientific notation expresses any number as a × 10ⁿ where 1 ≤ a < 10. Scientists use it to handle numbers like the speed of light or the mass of an atom.
The Format
Scientific notation: a × 10ⁿ
• a is a number from 1 to 9.999…
• n is an integer (positive for large numbers, negative for small)
Converting to Scientific Notation
Move the decimal until one non-zero digit is to the left. Count the moves — that is your exponent.
93,000,000 → 9.3 × 10⁷ (moved 7 places left)
0.000045 → 4.5 × 10⁻⁵ (moved 5 places right)
Multiplying in Scientific Notation
Multiply the a-values, add the exponents, then adjust if needed.
(3 × 10⁴) × (2 × 10³) = 6 × 10⁷
Real-World Scale
Speed of light ≈ 3 × 10⁸ m/s. Diameter of hydrogen atom ≈ 1.06 × 10⁻¹⁰ m. Scientific notation prevents mistakes when writing many zeros.
FAQ
Is 12 × 10³ correct scientific notation? No — a must be less than 10. Rewrite as 1.2 × 10⁴.
Quick Quiz
Test what you just learned. Choose the best answer for each question.