General Chemistry: Measurement, Significant Figures, and Scientific Notation

Measurement and Scientific Notation in Chemistry

Definition and Scope of Chemistry

Chemistry is the scientific discipline that seeks to understand the nature of matter by studying atoms and molecules. It encompasses the investigation of the composition, structure, properties, and changes of matter.

• Matter: Anything that has mass and occupies space.

• Atoms and Molecules: The fundamental building blocks of matter; atoms are the smallest units of elements, and molecules are combinations of atoms bonded together.

• Example: Water (H2O) is a molecule composed of two hydrogen atoms and one oxygen atom.

Decimal Representation and Scientific Notation

Scientific notation is a method used to express very large or very small numbers in a compact form, which is essential in chemistry for handling measurements and calculations.

• Decimal Representation: Moving the decimal point to convert between scientific notation and standard decimal form.

• Example: $1.201 \times 10^7 = 12,010,000$

• Scientific Notation: A number is written as $a \times 10^n$, where $1 \leq a < 10$ and $n$ is an integer.

• Example: $0.00005210 = 5.210 \times 10^{-5}$

Significant Figures

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

• Rules for Counting Significant Figures:

  1. All nonzero digits are significant.

  2. Zeros between nonzero digits are significant.

  3. Leading zeros are not significant.

  4. Trailing zeros are significant only if there is a decimal point.

• Example: The number 865,000 has 3 significant figures if written as $8.65 \times 10^5$.

• Example: $9.080 \times 10^4$ has 4 significant figures.

Estimating Digits and Uncertainty

In any measured number, the last digit is considered to be estimated, reflecting the uncertainty in the measurement.

• Example: In the number 48.93, the digit '3' is the estimated digit.

Calculations with Significant Figures

When performing calculations, the result should be reported with the correct number of significant figures based on the rules for addition/subtraction and multiplication/division.

• Addition/Subtraction: The result should have the same number of decimal places as the measurement with the fewest decimal places.

• Multiplication/Division: The result should have the same number of significant figures as the measurement with the fewest significant figures.

• Example: $106.92 \times 1.9 = 200$ (rounded to 2 significant figures)

• Example: $13.96 - 4.9102 + 71.5 = 80.5$ (rounded to 3 significant figures)

Metric Prefixes

Metric prefixes are used to denote powers of ten in the International System of Units (SI). The prefix 'pico' represents $10^{-12}$.

• Example: $1 \text{ picometer} = 1 \times 10^{-12} \text{ meters}$

Summary Table: Significant Figures and Scientific Notation

Concept	Example	Explanation
Scientific Notation	$5.210 \times 10^{-5}$	Expresses small numbers compactly
Significant Figures	865,000 (3 sig figs)	Precision in measurement
Metric Prefix: Pico	$10^{-12}$	Used for very small units