Accuracy and Precision of a Measurement

Biologists, ecologists, geneticists, and other life scientists all rely on measurements to make sense of the natural world. Whether you’re measuring the size of a cell under a microscope, the growth rate of plants in an experiment, or the migration speed of an animal tracked by GPS, the quality of your data depends on how accurate and precise your measurements are.

• Accuracy refers to how close a measured value is to the true or accepted value.

• Precision refers to how close repeated measurements are to one another, regardless of how close they are to the true value.

Let’s take a simple example: measuring the length of a leaf. Suppose your measuring tool is a digital caliper that gives values to the nearest 0.1 mm. You measure the same leaf three times and get: 84.1 mm, 84.2 mm, and 84.0 mm. These results are both accurate (if the actual length is about 84.1 mm) and precise (since the values are very close together).

Now imagine instead you record 82.0 mm, 92.3 mm, and 76.9 mm. These values vary a lot—low precision. Or you measure 79.5 mm three times, which is very consistent (high precision) but not close to the actual length (low accuracy).

Accuracy vs. Precision: Visualizing the Difference

Imagine you’re using a GPS collar to track the position of an endangered bird nesting in a wildlife preserve like in Figure 4.3, andFigure 4.4,.

 

Both cases can be problematic depending on the context. In science, we aim for measurements that are both accurate and precise.

Uncertainty in Calculated Results

When we make measurements and then use them in calculations—like area, volume, or reaction rates—those calculations also carry uncertainty. In biology and life sciences, this applies when calculating population densities, nutrient concentrations, enzyme reaction rates, or even field plot areas.

Let’s say you’re calculating the area of a rectangular leaf based on its measured length and width. Both measurements carry uncertainty, so your calculated area will too.

If your values have small uncertainties (typically a few percent or less), you can use the method of adding percent uncertainties:

For multiplication or division:
The percent uncertainty of the final result is the sum of the percent uncertainties in the measurements used.

Example: Calculating Leaf Surface Area

Suppose you measure a leaf as:

• Length = 4.00 cm with a 2% uncertainty

• Width = 3.00 cm with a 1% uncertainty

The area is:

$$A = \text{length} \times \text{width} = 12.0\ \text{cm}^2$$

The total percent uncertainty is:

$$2\% + 1\% = 3\%$$

So the uncertainty in area is:

$$0.03 \times 12.0 = 0.36 \approx 0.4\ \text{cm}^2$$

Final result:

$$A = 12.0 \pm 0.4\ \text{cm}^2$$

Check Your Understanding

A field biologist measures the time it takes two tagged turtles to cross a 10-meter stream. The stopwatch has an uncertainty of ±0.05 s. Turtle A finishes in 12.04 s, and Turtle B finishes in 12.07 s.
Can the stopwatch reliably tell which turtle was faster?

Answer: No—since the time difference (0.03 s) is smaller than the uncertainty (±0.05 s), the stopwatch is not precise enough to distinguish the two.

Precision of Measuring Tools and Significant Figures

Different measuring tools offer different levels of precision, meaning they can measure smaller increments.

• A ruler might measure to the nearest millimeter.

• A digital caliper might measure to the nearest 0.01 mm.

• A micropipette might dispense liquid in microliters (μL).

When recording a measurement, you can only report digits your tool allows you to measure, plus one estimated digit.

Example: If a microscope reticle lets you measure to the nearest 0.1 mm, and a bacterial colony falls between 2.2 mm and 2.3 mm, you might estimate the size as 2.25 mm. The “5” is an estimated digit.

Significant Figures (Sig Figs)

Significant figures are the digits in a measurement that carry meaning about its precision.

• All non-zero digits are significant.

• Zeros between significant digits are significant.

• Leading zeros are not significant (e.g., 0.0053 has 2 sig figs).

• Trailing zeros in a number with a decimal point are significant (e.g., 15.4500 has 6 sig figs).

• For ambiguous cases like 1300, use scientific notation (e.g., 1.30 × 10³ means 3 sig figs).

Example: 36.7 cm has 3 sig figs, while 0.00090 has 2 sig figs.

Significant Figures in Calculations

Multiplication/Division Rule:

• The result has the same number of significant figures as the measurement with the fewest sig figs.

Example:
Area of a petri dish:

$$r = 1.2\ \text{cm} \quad \Rightarrow \quad A = \pi r^2 = 4.5\ \text{cm}^2 \ (\text{2 sig figs})$$

Addition/Subtraction Rule:

• The result should have the same number of decimal places as the value with the fewest decimal places.

Example:

$$5.56\ \text{g} + 6.052\ \text{g} + 13.7\ \text{g} = 25.312\ \text{g} \Rightarrow \text{round to 0.1 g} \Rightarrow 25.3\ \text{g}$$

In This Textbook

To keep calculations clear and relevant:

• Most values use three significant figures, unless context demands more.

• Final answers reflect the least precise input value.

• Exact numbers (like “2” in

  $C = 2\pi r$C=2πr) do not affect significant figure rules.

Check Your Understanding

Q1: A researcher carries three samples of leaf litter: two weigh 13.5 g, and one weighs 10.2 g. What is the total mass?

A1: 13.5 + 13.5 + 10.2 = 37.2 g (Exact counts of items don’t affect sig figs.)

Q2: A lab slide accelerates on a tilted stage at 0.0255 m/s². If its mass is 55 kg, what is the net force?

$$F = m \times a = 55 \times 0.0255 = 1.4025\ \text{N} \Rightarrow \boxed{1.4\ \text{N}} \ (\text{2 sig figs})$$