Accuracy: 3.14 is a fairly accurate
approximation of π (pi).
Precision: 3.199 is a more precise approximation,
but it is less accurate.
Worked Example
Problem: The true length of a table is 2.00 meters. Three students measure it and get 1.99 m, 2.04 m, and 1.85 m. Which measurement is the most accurate?
Step 1: Find how far each measurement is from the true value of 2.00 m.
∣1.99−2.00∣=0.01
Step 2: Repeat for the second measurement.
∣2.04−2.00∣=0.04
Step 3: Repeat for the third measurement.
∣1.85−2.00∣=0.15
Answer: The measurement of 1.99 m is the most accurate because it has the smallest difference (0.01 m) from the true value.
Why It Matters
Accuracy matters whenever you need to judge whether an answer or approximation is good enough. In science, engineering, and everyday estimation, knowing how close your result is to the true value helps you decide whether to accept it or refine your method. For example, when rounding π to use in a formula, choosing 3.14 over 3.1 gives a more accurate calculation.
Common Mistakes
Mistake: Confusing accuracy with precision. Students often think more decimal places automatically means a better answer.
Correction: Precision refers to how many significant digits or decimal places a value has, while accuracy refers to how close it is to the true value. The value 3.199 has more decimal places (more precise) than 3.14, but 3.14 is closer to π ≈ 3.14159… and therefore more accurate.
Related Terms
Precision — How detailed a value is, distinct from accuracy
Mathwords