Pi Approximations — Definition, Formula & Examples
Pi approximations are simpler numbers used in place of the irrational number π ≈ 3.14159265… when an exact value isn't needed. Common approximations include 3.14, 22/7, and 355/113.
Since π is irrational (it cannot be expressed as a ratio of two integers and its decimal expansion never terminates or repeats), any numerical value used in computation is necessarily an approximation. Rational approximations such as and are convergents of the continued fraction expansion of π, providing increasingly accurate estimates with small denominators.
How It Works
Choose an approximation based on how much accuracy you need. For quick mental math, use . For slightly better accuracy with a simple fraction, use , which is accurate to about two decimal places. For remarkable precision from a fraction you can memorize, use , which is accurate to six decimal places. On tests, your teacher will usually tell you which value to use.
Worked Example
Problem: Estimate the circumference of a circle with radius 7 cm using 22/7 as an approximation for π.
Recall the formula: Circumference equals 2πr.
Substitute the approximation: Replace π with 22/7 and r with 7.
Simplify: The 7s cancel, leaving a clean result.
Answer: The circumference is approximately 44 cm. (Using a calculator with more digits of π gives about 43.982 cm, so the estimate is very close.)
Visualization
Why It Matters
Choosing the right approximation matters in construction, engineering, and science, where rounding errors can accumulate. In middle-school math, knowing that 22/7 and 3.14 are both approximations (not exact values) helps you understand why different problems give slightly different answers for circles.
Common Mistakes
Mistake: Believing that 22/7 is exactly equal to π.
Correction: 22/7 = 3.142857… while π = 3.141592…, so 22/7 is slightly larger than π. It is a useful approximation, not an exact value.