Measurement in Chemistry: Accuracy, Precision, and Significant Figures

Unit 1: Measurement in Chemistry

Accuracy and Precision

In scientific measurement, understanding the difference between accuracy and precision is essential for evaluating data quality and reliability.

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

• Precision: Describes how close repeated measurements are to each other, regardless of their closeness to the true value.

Example: Consider a set of dartboards:

• High precision, low accuracy: Darts are clustered together but far from the bullseye.

• High accuracy, low precision: Darts are spread out but average near the bullseye.

• High accuracy and high precision: Darts are clustered together at the bullseye.

Application Example: Four students measure the density of aluminum (true value: 2.7 g/mL). Their results are:

A	B	C	D
2.924	2.316	2.649	2.701
2.923	2.527	2.731	2.699
2.925	2.941	2.695	2.702
2.926	2.136	2.742	2.698
NA P	NA NP	A NP	A P

• A: Not accurate, but precise (values are close to each other, but not to 2.7).

• B: Not accurate, not precise.

• C: Accurate, not precise.

• D: Accurate and precise.

Measurement Terms: Percent Error and Deviation

To quantify accuracy, chemists use percent error:

$\text{Percent Error} = \frac{\text{Experimental Value} - \text{True Value}}{\text{True Value}} \times 100$

• Percent error indicates how close a measurement is to the true value.

• Percent deviation is another term for percent error.

Example: Measuring a 100.00 g standard weight:

• Measured value: 98.89 g

• Percent deviation: $\frac{98.89 - 100.00}{100.00} \times 100\% = -1.11\%$

Measurement Terms: Precision and Range

Precision is often evaluated by the range of repeated measurements:

$\text{Range} = \text{Highest value} - \text{Lowest value}$

• Smaller range = higher precision.

• Example: Four measurements of 100.01, 100.00, 99.99, 100.00 g have a range of 0.02 g (high precision).

To express uncertainty, the range is often divided by 2 and reported as ± value.

Significant Figures

Significant figures (sig figs) are the digits in a measurement that are known with certainty plus one estimated digit. They reflect the precision of a measurement.

• All nonzero digits are significant. (e.g., 1234 has 4 sig figs)

• Zeros between nonzero digits are significant. (e.g., 1.003 has 4 sig figs)

• Leading zeros are not significant. (e.g., 0.0025 has 2 sig figs)

• Trailing zeros are significant if there is a decimal point. (e.g., 2.300 has 4 sig figs; 2300 has 2 sig figs unless written as 2.300 × 103)

Significant Figures in Calculations

• Multiplication/Division: The result should have as many sig figs as the value with the least number of sig figs.

• Addition/Subtraction: The result should have as many decimal places as the value with the least number of decimal places.

Example (Addition):

• 3.461728 + 14.91 + 0.980001 + 5.2631 = 24.614829

• 14.91 has the least decimal places (2), so the answer is rounded to 24.61

Example (Multiplication):

• 64 × 12.458 = 796.352

• 64 has 2 sig figs, so the answer is rounded to 80 (if using scientific notation, 8.0 × 101)

Rounding Off Rules

• Identify the digit to round to (based on required sig figs).

• If the next digit is 0–4, round down (leave the digit the same).

• If the next digit is 5–9, round up (increase the digit by 1).

Example: Round 3.34237 × 104 to 2 sig figs: 3.3 × 104

Example: Round 2.3467 × 103 to 3 sig figs: 2.35 × 103

Conversion Factors

Conversion factors are used to change units in measurements without changing the value.

• Set up as: Given Quantity × Conversion Factor = New Quantity

• Example: How many meters in 54 cm?

$54\ \text{cm} \times \frac{1\ \text{m}}{100\ \text{cm}} = 0.54\ \text{m}$

• Example: How many milligrams in 0.53 kg?

$0.53\ \text{kg} \times \frac{1000\ \text{g}}{1\ \text{kg}} \times \frac{1000\ \text{mg}}{1\ \text{g}} = 530,000\ \text{mg}$

Exponential (Scientific) Notation

Scientific notation expresses very large or small numbers as a product of a number (between 1 and 10) and a power of 10.

• 1,000 = $1 \times 10^3$

• 0.001 = $1 \times 10^{-3}$

• 2,386 = $2.386 \times 10^3$

• 0.0123 = $1.23 \times 10^{-2}$

Summary Table: Accuracy vs. Precision

	Accurate	Inaccurate
Precise	Close to true value, measurements close together	Measurements close together, but far from true value
Not Precise	Average near true value, measurements spread out	Measurements spread out, far from true value

Additional info: These foundational concepts are essential for all laboratory and theoretical work in chemistry, as they ensure data is interpreted and reported correctly.