Scientific Notation Rules
Multiply: multiply coefficients, add exponents. Divide: divide coefficients, subtract exponents. Add/Subtract: align exponents first (adjust coefficient of the smaller), then add/subtract coefficients. Always normalize the result so the coefficient is between 1 and 10.
Frequently Asked Questions
Scientific notation expresses numbers as a coefficient (1 ≤ a < 10) multiplied by a power of 10. For example: 0.000045 = 4.5 × 10⁻⁵ and 6,200,000 = 6.2 × 10⁶. It is used in science and engineering to handle very large or very small numbers conveniently.
Move the decimal point left or right until you have one non-zero digit before the decimal. Count the number of places you moved. If you moved left, the exponent is positive; if right, it is negative. Example: 0.0047 → move decimal 3 places right → 4.7 × 10⁻³.
Multiply the coefficients and add the exponents: (a × 10ⁿ) × (b × 10ᵐ) = (a×b) × 10ⁿ⁺ᵐ. Then adjust if the coefficient is not between 1 and 10. Example: (3 × 10⁴) × (2 × 10³) = 6 × 10⁷.
Divide the coefficients and subtract the exponents: (a × 10ⁿ) / (b × 10ᵐ) = (a/b) × 10ⁿ⁻ᵐ. Example: (9 × 10⁶) / (3 × 10²) = 3 × 10⁴.
First convert both numbers to the same power of 10, then add or subtract the coefficients. Example: 3.5 × 10⁴ + 2.0 × 10³ = 3.5 × 10⁴ + 0.2 × 10⁴ = 3.7 × 10⁴.
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