Absolute , Relative, Percentage Error Examples

 1. Determine the absolute and relative errors when approximating p by p∗ when

(a) p = 0.3000 × 101 and p∗ = 0.3100 × 101;

(b) p = 0.3000 × 10−3 and p∗ = 0.3100 × 10−3;

(c) p = 0.3000 × 104 and p∗ = 0.3100 × 104.

Case (a)

Absolute error: |0.3000 × 101 - 0.3100 × 101| = 0.1000 × 101 = 10

Relative error: |0.3000 × 101 - 0.3100 × 101| / |0.3000 × 101| = 0.3333333333333333

Case (b)

Absolute error: |0.3000 × 10−3 - 0.3100 × 10−3| = 1.0000000000000026 × 10−5

Relative error: |0.3000 × 10−3 - 0.3100 × 10−3| / |0.3000 × 10−3| = 0.03333333333333342

Case (c)

Absolute error: |0.3000 × 104 - 0.3100 × 104| = 100

Relative error: |0.3000 × 104 - 0.3100 × 104| / |0.3000 × 104| = 0.03333333333333333

As you can see, the absolute error is the same in all three cases, but the relative error is different. The relative error is smallest in case (a), where the value of p is relatively large. The relative error is largest in case (c), where the value of p is relatively small.