TeXipedia

approx

Denotes approximate equality or an estimation between mathematical expressions or values.

Overview

Essential in mathematical writing where exact equality cannot be established or is unnecessary for the context at hand. Widely used across scientific disciplines:

  • Common in numerical analysis when discussing computational approximations
  • Appears in physics when dealing with experimental measurements and uncertainties
  • Used in statistics when describing estimated parameters or sample statistics
  • Helpful in engineering calculations where precise values are impractical or unnecessary

Particularly valuable when discussing convergent series, numerical methods, or when rounding complex calculations to practical precision levels.

Examples

Expressing an approximate numerical value.

π≈3.14159\pi \approx 3.14159 
\pi \approx 3.14159

Showing approximate equality in a physical equation.

E=mc2≈9.0×1016 joulesE = mc^2 \approx 9.0 \times 10^{16} \text{ joules} 
E = mc^2 \approx 9.0 \times 10^{16} \text{ joules}

Indicating an asymptotic relationship in mathematics.

f(n)≈n2 as n→∞f(n) \approx n^2 \text{ as } n \to \infty 
f(n) \approx n^2 \text{ as } n \to \infty