Question

Is an area calculation exact when you use 3.14 or 22/7 as a value for π Explain.

Answer 1

No — using 3.14 or 22/7 does not give an exact area. π is an irrational number (it cannot be written exactly as a fraction or a finite decimal), so any finite decimal or simple fraction is only an approximation of π.

Some details:
- 3.14 is a decimal approximation of π and is a little smaller than π. Its relative error is about (3.14 − π)/π ≈ −0.0506% (about 0.000506 in fractional terms).
- 22/7 = 3.142857... is a rational approximation a little larger than π. Its relative error is about (22/7 − π)/π ≈ +0.04025%.

Because the area of a circle is A = πr^2, the percentage error in the area when you replace π by an approximation equals the percentage error of the approximation itself. For example with r = 10:
- exact area = π·100 ≈ 314.1593
- using 3.14 → 314.00 (about 0.0506% low)
- using 22/7 → 314.2857 (about 0.0403% high)

For most practical measurements these approximations are fine, but they are not mathematically exact. If you need higher accuracy, use more digits of π or a better rational approximation (for example 355/113 is extremely close to π).