Convert between decimal and scientific notation, or perform arithmetic with scientific notation.
Scientific notation expresses numbers as a coefficient between 1 and 10 multiplied by a power of 10 (a × 10^b). It is essential for representing very large or very small numbers compactly.
a × 10^b where 1 ≤ |a| < 10. Multiplication: (a₁×10^b₁)(a₂×10^b₂) = (a₁×a₂)×10^(b₁+b₂). Division: (a₁×10^b₁)/(a₂×10^b₂) = (a₁/a₂)×10^(b₁−b₂).
Move the decimal point so that there is exactly one non-zero digit to its left. Count the moves: right moves give a negative exponent, left moves give a positive exponent. For example, 0.000123 = 1.23 × 10⁻⁴.
First adjust exponents to match, then add the coefficients. For example, 2.5×10⁴ + 1.2×10³ = 2.5×10⁴ + 0.12×10⁴ = 2.62×10⁴ = 26200.