Accuracy, precision, and significant figures are fundamental concepts in scientific measurements. They help describe the reliability and quality of measurements and data. Here’s a detailed look at each of these concepts:
1. Accuracy:
Accuracy refers to how close a measured or observed value is to the true or accepted value, often called the “ground truth.” In other words, accuracy measures how well a measurement represents the actual physical quantity. Accuracy is a qualitative assessment of correctness.
Example: If a thermometer reads 98.6°F for a person’s body temperature and the actual body temperature is 98.6°F, the measurement is considered accurate.
2. Precision:
Precision, on the other hand, quantifies the degree of consistency or reproducibility in measurements. It measures how closely individual measurements agree, regardless of their proximity to the true value. High precision indicates repeated measurements provide similar results, even if they are not close to the actual value.
Example: If a scale consistently measures the same object as 10.01 grams, 10.02 grams, and 10.01 grams in repeated measurements, it demonstrates high precision.
3. Significant Figures:
Significant figures (sig figs or SF) are the digits in a measurement that provide information about its precision. They include all certain digits (digits known with certainty) and one uncertain or estimated digit. Significant figures help express the precision of a measurement and ensure that results are reported with appropriate uncertainty.
Rules for Determining Significant Figures:
– All nonzero digits are considered significant. For example, in the number 345, all three digits are significant.
– Any zeros between significant digits are also significant. In 1005, there are four significant figures.
– Leading zeros (zeros to the left of the first nonzero digit) are not considered significant. In 0.045, there are two significant figures.
– Trailing zeros (zeros to the right of nonzero digits and after the decimal point) are considered significant. In 3.50, there are three significant figures.
– Exact numbers, such as those obtained by counting or defined quantities, have infinite significant figures. For example, there are exactly 12 eggs in a dozen.
Significant Figures in Calculations:
When performing mathematical operations, it’s essential to follow the rules for significant figures to maintain precision:
– The result should be rounded to the least decimal places in the original values in addition and subtraction.
– In multiplication and division, the result should have the same number of significant figures as the value with the fewest significant figures in the calculation.
Using Accuracy, Precision, and Significant Figures:
– In scientific experiments, the goal is to achieve accuracy and precision. A measurement close to the true value (accurate) and consistent across repeated trials (precise) is highly desirable.
– Reporting results with the appropriate number of significant figures communicates the precision of the measurement and helps avoid the impression of unwarranted accuracy.
– Researchers should be aware of and manage errors to improve the accuracy and precision of their measurements and experiments.
