Number approximations

Approximating a number means replacing it with another number that is close to it, often to simplify calculations or because the exact value is unknown or unnecessary. Approximations can be made by rounding, truncating, or using simpler fractions or decimals.

Important properties

• The error of an approximation is the difference between the exact value and the approximation.

• Approximations can be specified to a certain degree of accuracy (e.g., to the nearest $0.01$).

• Some numbers, like $\pi$ or $\sqrt{2}$, cannot be written exactly as decimals or fractions, so we use approximations.

• Approximations are used in estimation, measurement, and when working with irrational or repeating decimals.