Error and Approximation
In mathematics and real life, we often work with values that are close to the exact answer but not perfectly precise. Understanding approximation and error helps us know how accurate our answers really are!
What is Approximation?
An approximation is when we use a close, simpler value instead of the exact one.
Common Approximations:
- π ≈ 3.14 (pi is actually 3.14159265...)
- √2 ≈ 1.41 (actually 1.41421356...)
- √3 ≈ 1.73 (actually 1.73205080...)
Symbol: We use ≈ to mean "approximately equal to"
Key Idea: ALL measurements in real life are approximations! When you measure your height, the ruler gives an approximate value.
Exact vs Approximate Values
Exact Values
- ⅓ (one-third)
- √5
- π
- ⅔
Approximate Values
- 0.333
- 2.236
- 3.14159
- 0.667
Why approximate? Sometimes exact values are impossible to write as decimals (like π) or impractical to use in calculations.
What is Error (Погрешность)?
Error is the difference between the exact value and the approximate value. It shows how far our approximation is from the true value.
Error Formula:
Error = |Exact Value − Approximate Value|
The vertical bars | | mean "absolute value" (always positive) Interactive visualization — available in the full lesson