CHEM104 Lecture Chapter 1 Overview: Significant Figures

Importance of Significant Figures in Chemistry

• Chemistry relies heavily on measurements, which are not exact.
• Significant figures help communicate which digits in a measurement are certain and which are estimated.

Recording Significant Figures

• Record all certain digits plus the first estimated digit in a measurement.
• Example: Measuring length with a ruler, record up to the smallest unit marked and estimate the next digit.

Examples of Measurement

• If a pink line falls between 4.2 cm and 4.3 cm, record as 4.25 cm (or similar) because the '4' and '2' are certain, and the '5' is estimated.
• Always estimate one digit past the smallest marking on the instrument.

Understanding Measurement Precision

• Measurement such as 4.00 cm implies measurement precision to the hundredths place, not merely 4 cm.
• No measurement is exact; counting (e.g., 5 fingers) can be exact by definition.

Rules for Counting Significant Figures

1. Captured Zeros: Always significant. E.g., in 102.5, the zero is significant.
2. Leading Zeros: Never significant. E.g., in 0.00125, the zeros are not significant.
3. Trailing Zeros: Significant only if there's a decimal point. E.g., 120 has 2 significant figures, but 120.0 has 3.

Exact Numbers

• Numbers can be exact by definition (e.g., 12 inches in a foot) or by counting (e.g., 3 repetitions of an experiment).
• Exact numbers have an infinite number of significant figures.

Rules for Mathematical Operations

• Addition/Subtraction: Result should have the same number of decimal places as the measurement with the least.
  • Example: Adding 23.573 g and 0.15 g equals 23.723 g, rounded to 23.72 g.
• Multiplication/Division: Result should have the same number of significant figures as the measurement with the least.
  • Example: Multiplying 5.75 cm by 0.50 cm gives 2.875 cm², rounded to 2.9 cm².

Rounding Rules

• If the first digit to be dropped is 0-4, round down; if 5-9, round up.
• Example: 23.723 becomes 23.72 because the digit '3' is less than 5.

By following these guidelines, you ensure accuracy and precision in chemical measurements and calculations.