Precision
Precision
The level of detail in a number or estimate. A precise number has many significant digits. Note: An answer may be precise without being accurate.
Accuracy: 3.14 is a fairly accurate approximation of π (pi).
Precision: 3.199 is a more precise approximation, but it is less accurate.
Example
Problem: A lab group measures the length of a rod that is exactly 25.0 cm long. Three students report the following measurements: Student A says 25.1 cm, Student B says 25.132 cm, and Student C says 28.4291 cm. Compare the precision and accuracy of each measurement.
Step 1: Count the significant digits in each measurement to judge precision.
A: 25.1 (3 sig. digits)B: 25.132 (5 sig. digits)C: 28.4291 (6 sig. digits)
Step 2: Rank by precision (most significant digits = most precise): C is the most precise, B is next, A is least precise.
Step 3: Now check accuracy by finding each measurement's error from the true value of 25.0 cm.
∣25.1−25.0∣=0.1∣25.132−25.0∣=0.132∣28.4291−25.0∣=3.4291
Step 4: Rank by accuracy (smallest error = most accurate): A is the most accurate, B is next, and C is the least accurate despite being the most precise.
Answer: Student C's measurement (28.4291 cm) is the most precise because it has the most significant digits, but it is the least accurate because it is farthest from the true value. Student A's measurement (25.1 cm) is the least precise but the most accurate. This shows that precision and accuracy are independent qualities.
Frequently Asked Questions
What is the difference between precision and accuracy?
Accuracy describes how close a value is to the true or accepted value. Precision describes how much detail a value contains—essentially how many significant digits it has. You can be precise without being accurate (e.g., 3.1492 as an estimate of π is precise but less accurate than 3.1416), and you can be accurate without being precise (e.g., 3.1 is a rough but fairly accurate estimate of π).
Does more decimal places always mean more precision?
More decimal places generally indicate more precision, but only if those digits are meaningful. Trailing zeros or digits added without justification from measurement don't add real precision. For example, writing 5.00 implies three significant digits and is more precise than writing 5, but writing 5.000000 is only meaningful if your measuring tool can actually resolve to that level of detail.
Precision vs. Accuracy
Precision refers to how detailed or specific a number is (how many significant digits it uses). Accuracy refers to how close a number is to the true value. A measurement of 3.14159 for π is both precise and accurate. A measurement of 3.19999 for π is precise (5 significant digits) but not accurate (it's far from the true value). A measurement of 3.1 for π is accurate (close to the true value) but not very precise. The two qualities are independent: improving one does not guarantee improvement in the other.
Why It Matters
Understanding precision helps you interpret data and measurements correctly. In science, reporting a result as 9.80665 m/s² communicates a very different level of confidence than reporting 9.8 m/s². When you combine measurements in calculations, the precision of your answer should match the least precise input—this is why significant digit rules exist.
Common Mistakes
Mistake: Assuming that a more precise number is automatically more accurate.
Correction: Precision and accuracy are independent. A value like 7.23841 can be very precise yet far from the true value. Always check closeness to the true value separately from the number of significant digits.
Mistake: Adding extra decimal places to make an answer look better.
Correction: Extra digits are only meaningful if they come from actual measurement or calculation. Writing 4.000 when your tool only measures to the nearest whole number is false precision and misleads anyone reading your result.
Related Terms
- Significant Digits — The digits that determine a number's precision
- Accuracy — Closeness to the true value, distinct from precision
- Pi — Classic example for comparing precision and accuracy
- Rounding — Reduces precision by removing significant digits
- Estimation — Produces approximate values with limited precision
- Decimal — Decimal places contribute to a number's precision