Measurement, SI Units, Scientific Notation, and Significant Figures in General Chemistry

Units of Measurement: SI System

Introduction to SI Units

In chemistry, measurements are fundamental for quantifying observations and performing calculations. The International System of Units (SI) provides a standardized set of base units for scientific measurements, ensuring consistency and clarity across disciplines.

• Qualitative observations describe qualities (e.g., color).

• Quantitative observations involve measurements (e.g., mass, volume).

SI Base Units

The SI system defines seven base units for fundamental quantities:

Quantity	Unit	Symbol
Length	Meter	m
Mass	Kilogram	kg
Time	Second	s
Temperature	Kelvin	K
Amount of substance	Mole	mol
Electric current	Ampere	A

Derived Units

Derived units are combinations of base units used for other quantities:

Quantity	Unit	Symbol	In terms of base units
Energy	Joule	J	$1\,J = 1\,kg\cdot m^2/s^2$
Volume	Liter	L	$1\,L = 1000\,mL$ $1\,mL = 1\,cm^3$

Prefix Multipliers: Adjusting the Scale of Units

SI Prefixes and Their Conversion Factors

SI prefixes are used to express measurements at different scales. Memorizing these prefixes is essential for converting between units.

Prefix	Symbol	Conversion factor (using meter as example)
Exa	E	1 Em = $10^{18}$ m
Peta	P	1 Pm = $10^{15}$ m
Tera	T	1 Tm = $10^{12}$ m
Giga	G	1 Gm = $10^9$ m = 1,000,000,000 m
Mega	M	1 Mm = $10^6$ m = 1,000,000 m
Kilo	k	1 km = $10^3$ m = 1,000 m
Deci	d	1 dm = $10^{-1}$ m
Centi	c	1 cm = $10^{-2}$ m
Milli	m	1 mm = $10^{-3}$ m
Micro	μ	1 μm = $10^{-6}$ m
Nano	n	1 nm = $10^{-9}$ m
Pico	p	1 pm = $10^{-12}$ m
Femto	f	1 fm = $10^{-15}$ m
Atto	a	1 am = $10^{-18}$ m

Standard Scientific Notation

Expressing Numbers in Scientific Notation

Scientific notation is used to represent very large or very small numbers in a compact form. The general format is:

• $A \cdot 10^n$ where $1 \leq A < 10$ and $n$ is an integer.

• If the exponent is positive, move the decimal to the right.

• If the exponent is negative, move the decimal to the left.

Example: $5.32 \times 10^3$ L = 5320 L

Example: $2.4 \times 10^{-6}$ mol = 0.0000024 mol

Converting Between Scientific Notation and Ordinary Numbers

• To convert to scientific notation, count the number of places the decimal moves to create a coefficient between 1 and 10.

• To convert from scientific notation to ordinary numbers, move the decimal according to the exponent.

Unit Conversions Using Prefix Multipliers

Converting Between Units

Unit conversions often require multiplying by appropriate powers of ten based on SI prefixes.

• Set up conversion factors so that units cancel appropriately.

• Always report final answers in scientific notation when required.

Example: Convert 19.05 mm to μm:

• $19.05\,mm \times \frac{1\,m}{10^3\,mm} \times \frac{10^6\,μm}{1\,m} = 1.905 \times 10^4\,μm$

Uncertainty in Measurement (Significant Figures)

Understanding Significant Figures

All measurements have some degree of uncertainty. Significant figures reflect the precision of a measurement, including all certain digits and the first uncertain digit.

• Estimated digit: The last digit in a measurement, which is uncertain.

• Report measurements to the correct number of significant figures, based on the instrument's precision.

Example: Reading a graduated cylinder: If the meniscus is between 20 and 21 mL, and you estimate 20.14 mL, the '4' is the uncertain digit.

Precision and Accuracy

Precision refers to the reproducibility of measurements, while accuracy describes how close a measurement is to the true value.

• Precision: Degree of agreement among several measurements of the same quantity.

• Accuracy: Agreement of a measured value to the true value.

Example: Multiple measurements of mass with a balance. More decimal places indicate higher precision.

Comparing Precision and Accuracy

Student	Trial 1	Trial 2	Trial 3	Average ± Standard Deviation
Student A	10.49 g	9.78 g	10.00 g	10.1 ± 0.3 g
Student B	9.78 g	9.78 g	9.79 g	9.78 ± 0.01 g
Student C	10.00 g	10.00 g	10.00 g	10.00 ± 0.00 g

• Student C is both accurate and precise (values close to true value and little spread).

• Student B is precise but not accurate (values close together but not close to true value).

• Student A is neither accurate nor precise.

Counting Significant Figures

Rules for Significant Figures

• Nonzero integers are always significant.

• Leading zeros never count (e.g., 0.0061 has 2 sig figs).

• Captive (interior) zeros always count (e.g., 2033 has 4 sig figs).

• Trailing zeros are significant only if there is a decimal point (e.g., 652.70 has 5 sig figs).

Example: 0.000032 has 2 significant figures.

Example: 111.05 mL has 5 significant figures.

Summary Table: Significant Figure Rules

Type of Zero	Significant?	Example	Sig Figs
Leading	No	0.0061	2
Captive	Yes	2033	4
Trailing (with decimal)	Yes	652.70	5
Trailing (no decimal)	No	100	1

Practice and Application

• Always report measurements with the correct number of significant figures.

• Use scientific notation for very large or small numbers.

• Apply SI prefixes for unit conversions.

Example: Convert 0.0062 to scientific notation: $6.2 \times 10^{-3}$

Example: Convert 1,210 to scientific notation: $1.21 \times 10^3$

Additional info: These foundational concepts are essential for all subsequent topics in General Chemistry, including stoichiometry, solution preparation, and quantitative analysis.